Semiotic Cognitive Information Processing:
Learning to Understand Discourse.
Burghard B. Rieger1
Computational Linguistics, University of Trier
rieger@ldv.uni-trier.de
In response to deficits encountered likewise in computational linguistics (CL), artificial intelligence research (AI) and cognitive psychology (CP) whose theoretical and applicational problems in understanding natural language information processing by men and machine are becoming exceedingly pressing, the last two decades saw a certain renaissance in semiotics. The new interest in the cognitive foundations of sign organization and manipulation processes was spurred even further by artificial life research (AL) and the quest for a principled theory of understanding symbols and languages, models and (re)presentations, simulations and realizations. Such a theory is expected to supply some grounding also for knowledge acquisition as a conception of learning whose formal derivation, procedural instanciation, and testable results provide some symbol and language independent evidence of what can be (said to be) understood.
Following these introductory remarks (1.) will be a short characterization of the cognitive view (2.) to language understanding and the lay-out of a system theoretical frame for cognitive processing (3.), before on the grounds of both the computational semiotics perspective (4.) of memory, knowledge, and understanding is developed. Introducing the functional relevancy of language structures (5.) and their granular decomposition will set the stage for an empirical reconstruction (6.) and the experimental testing (7.) of the (tentative) design and (implemented) modeling of a semiotic cognitive information processing (SCIP) system whose testable language understanding performance is considered an instanciation of enactive learning as summarized in the conclusion (8.).
The semiotic perspective is not to be confused with Newell's physical symbol system hypothesis4 (PSSH) (cite Newell80) which gave rise to the computer metaphor (cite MillerJohnsonL76) that rests on the suggestive resemblance between mind and computer and served as a guideline in early cognitive sciences (cite JohnsonLWas77). It tends to determine even recent models of cognitive systems and natural language processing (RickheitHabel99) in hiding, rather than addressing the central issues by presupposing an immediate understanding of what in fact stands in need of mediated explanation5. Hence, some of the computer metaphor's seminal conceptual distinctions and their terminological derivatives will in the sequel be employed where necessary to bring home our issue in revising them.
A case in point is the notion of mental models conceived as internal images or representations of those (structures of) entities external to the cognitive system. They are said to correspond to that very segment (or layer of the organization) of the real world the system has to adapt to, or has to control in order to survive. In presupposing the duality of the mind/matter division to be fundamental, most cognitive models and their explication of natural language understanding (as well as nearly all realistic theories and models of referential semantics) readily identify - in accord with PSSH - mental images (or internal representations) of the external world with what natural language expressions may convey when understood. Consequently, cognitive processing and understanding of natural language expressions in particular is hypothesized to be modeled as a mapping of percepts and/or language structures onto mental images or internal representations. As their relations to the external world are pre-established by definition, the mental images' (semantic) interpretability is unquestionable and seems to justify them being named meanings.
Accordingly, understanding meanings appears to be a form of cognitive processing conceived as an activity that (somehow) relates certain (structures of) entities (e.g. objects, signs) observed in reality, to concepts and conceptual structures (e.g. mental images, internal representations) in the mind that are not directly observable. This observational deficit apparently was not considered too serious an impediment as it could easily be compensated by the core assumption the PSSH had formulated, namely, that internal images and their conceptual relations can be represented as (or even have the structure of) propositions. This made the whole framework available to the cognitive study of conceptual structures which logics and linguistics had so far developed and successfully employed as analytical and representational tools for language structures (up to the sentence boundary), with the additional advantage that the formats of representational results from cognitive analyses of mental structures (mind) and those from linguistic6 analyses of language structures (meaning) would be the same. Although an identification on apparently hypothetical grounds, it nevertheless gave rise also to what has come to be named rather euphemistically linguistic transparency as postulated both in cognitive psychology and cognitive linguistics.
Although this notion had been questioned since the advent of new connectionism (cite Pfeiffer89) and has come under severe critique only recently for various reasons (cite RieglerPS99), it is surprising to find that the hypothetical character of the assumptions underlying the linguistic transparency postulate could have been overlooked, fallen into oblivion, or - for whatever reason - kept aside for quite a while. Thus, there was very sparse inquiry into how the postulated mental images, conceptual structures, or internal representations are constituted in the first place, i.e. which (adaptive, learning, emergent, etc.) processes do in fact enable a cognitive system to acquire these structures (propositional or whatever else may serve their purpose) and/or how their relatedness to the external world was established. Nor was there, in the second place, any serious interest - given the internal structures and their external relations were not considered innate, propositional, or else unquestionable, but instead subject to emergence and/or modification - to investigate how these structures (or those others that serve their purpose) can be (re)constructed or realized by procedural models of cognitive processing in language understanding. It simply did not occur to ask by way of which class of processes a material entity (sign structure) is not only perceived as such in order to be related to given internal models, but also realized in its (semiotic) functions which instead yield emergent internal representations.
Traditional models of cognitive language information processing (CLIP) do not answer questions that their designers had never been interested in until challenged by developments in the field applied to intelligence and language understanding (cite[pp. 11] RatschStamatescu98). What can nevertheless be derived as their response to the above problems, boils down to the general assumption that knowledge of various kinds7 has to be postulated in order to let the cognitive processes operate the way they do in both, the natural system and its models. The obvious but unwarranted readiness to identify the properties of models (or explicatum) whose adequacy is pretended instead of tested, with features of the original (or explicandum) that ought to be isolated in order to be explained, is one of the reasons that the so-called cognitive paradigm could not really be of help in overriding the presupposed mind/matter duality which keeps on to determine most procedural approaches to language understanding both in its rule based, symbolic, 'linguistically transparent' type, as well as in its pattern based, distributed, connectionist type of modeling.
Challenging this duality for the object of modeling (natural language understanding)8, not, however, for the modeling activity (repeatedly reproducible mediation)9 , it will be argued that there are cognitive processes which not only cut across the distinction of mind and matter, but can even be considered to underlie and allow for this distinction. A class of these processes may be studied on the grounds of observable structures of natural language discourse in situated communicative interaction. These may procedurally be modeled given (and providing for) a possibility to distinguish an internal or endo- from an external or exo-view of reality which - in replacing the mind/matter duality - might (but need not) be identical.
In the cognitive sciences, representations are taking a number of (even conflicting) functions which is the case with mental models. These either serve an explanatory purpose (allowing to understand how cognitive systems might manage to control complex input-output relations the way they do), or are in need of explanation themselves (as resulting from perceptions of the external world, and how these perceptions are transformed to gain a status of structures, which may be stored, identified, retrieved, and reactivated to serve the purpose they do). According to Johnson-Laird mental models play
a central and unifying role in representing objects, states of affairs, sequences of events, the way the world is, and the social and psychological activities of daily life. They enable individuals to make inferences and predictions, to understand phenomena, to decide what actions to take and to control its execution, and above all to experience events by proxy: they allow language to be used to create representations comparable to those deriving from direct acquaintance with the world; and they relate words to world by way of conception and perception.'' (cite[p. 397] JohnsonLaird83)The encompassing range of commitments listed here is but an illustration of the far reaching claims which mental models in cognitive science were expected to satisfy as internal representations of the external world both of the original/natural and the modeled/artificial cognitive system10. Apparently, these conditions were easily met as specified by the PSSH, so that symbolically formatted, propositional, language-like representations of conceptual systems (mind) formalized by logic-based calculi provided the interpreted structures whose interpretability did not seem to be in need of derivation or mediation11 establishing their representational relation to what they stand for or symbolize (matter).
Following cognitive linguistics as being concerned with the (theoretical, formal, empirical, descriptive, normative, quantitative, procedural, etc.) analysis of natural languages, and linguistic semanticists in particular who are interested in how natural language expressions convey the meaning and informational contents they have, there is - by and large - some agreement on fundamentals that are fairly undisputed (although differently weighted in the wide spectrum of semantic theories). This accord appears to be based on the (minimal) assumption that language signs have (to have) meanings to let them be conveyed in communication among (natural or artificial) cognitive systems which need to have the knowledge to understand them. This wording of seemingly common sense trivialities nevertheless comprises a complex of multiply nested constraints and mutual dependencies which have been addressed under the notions of situatedness and attunement, grounding and embodiment introduced below (see pp. and ). These terms relate to central properties which apparently refer to several aspects of what in semiotics has been known as semiosis13 . What appears to be the core problem of modeling language understanding as a cognitive process of meaning constitution can be specified as a cognitive system's grounding or an agent's embodiment (see pp. ). Its semiotic features and its systems theoretical conditions go far beyond what model designers (of disembodied artificial cognitive systems) have mastered so far which people (as naturally embodied cognitive systems) have and apparently satisfy when using language expressions to communicate results of their cognitive processing successfully.
As traditional approaches consider disembodiment if not a prerequisite then at least an epistemological condition for the development of experimental models which are empirically testable, it might well turn out that only under this assumption natural and artificial cognitive language information processing systems (CLIP) can be defined as modular being composed of discernible strata of interacting subsystems. These have quite successfully been specified as knowledge of language signs (vocabulary), of structures of their combinability to form terms and strings of terms (syntax), of meanings of these terms and their compositions (semantics), and of how to employ all this adequately (rules and patterns) in situations (pragmatics). The hypothesis is that functional co-operation among these strata enables the CLIP system's successful conveyance of information to others (communicating)14. As most of these modules vary in bulk and condition, depending on co- and contextual constraints which are subject to changes of (individual, social, collective) knowledge that is permanently modified by cognitive performance (learning/forgetting, activity/idleness, etc.), the dynamism of multiply interacting dependencies poses severe problems not only (but essentially) to realistic semantics whose propositional conception of static knowledge, symbolic representations, and rule-based processing does not (yet) allow to cope with it adequately.
Having identified (formal) language to be central for this way of modeling approach to cognition, only the more pressing becomes the quest for answers to the many questions which (natural) language understanding poses but symbol systems - in presupposing the employed signs' meanings being understood - do not even allow to word.
What has been termed the Cartesian (cite Atmannspacher96) or epistemic cut (cite Pattee96) reflects upon the cognitive dilemma which the physicists' paradigm of scientific analyses produces whenever it is applied to CLIP systems. These require - unlike complex dynamic systems in physics - a form of measurement, memory, and selection, none of which are functionally describable by physical laws that ... are based on energy, time, and rates of change.'' (cite Pattee96). The argument is again about what realists (cite Putnam91) call reality and its representations (cite RieglerPS99) and how the partition which separates (observable) objects or entities from the (observing) system which perceives them and brings about such a partitioning, can be understood more as a result of the system's cognitive activities rather than a presupposition to them. The scope of questions narrows down on how the relation between the system and its embedding environment can be made the basis it probably provides for the analyses of cognitive processes. This relation which underlies such notions like grounding and embodiment, attunement and situatedness appears to be central also for a more adequate understanding of signs, symbols, and languages, and what their communicative employment creates and presents rather than represents and depicts. Understanding language understanding from a systems theoretical perspective will hopefully improve the modeling too that has to be developed for processes which constitute understanding as a form of learning, and which are yet more enigmatic than well understood.
In many cases, such a reduction is indeed indicated and well suited, provided the model designers knowledge (of external environmental constraints and/or internal systemic architectures) is sufficiently certain and reliably precise to model a system's respective internal processing or external behavior. In cases where this knowledge either cannot be assumed or is disputed and not well understood, research is most advised to investigate its conditions and to look for processes which might ground, if not generate it. In model theoretic semantics and its employment in cognitive language information processing (CLIP), this chance is far too often missed15 . Even approaches which combine the system's modular organization (b) and its observable performance (a) do not suffice unless, of course, the focus is on the system's interaction with its environment constituting the system-environment (SE) relation.
It has to be noted, though, that percept structures - albeit a result of input processing and hence a form of output - have not to be externalized (as Fig. 2 might suggest). Their separation is merely to indicate a difference of the system's experience resulting in a percept structure (knowledge what) which is (re)presented in some format distinct from other results of processing that present themselves as a change of the system's internal state (knowledge how). Although both are internal to the system, the latter is without alternative whereas the former, when stored in separately structured memory modules for (identifiable and selective) retrieval, allows for this very possibility of alternative system states being invoked by (internal) memory representations rather than by external perturbations. With respect to evolutionary systems, the complementary functions - classification fulfilled in acts of measurement which serve to interpret the meanings of their representation - have been identified as an epistemological necessity (cite[p.270] Pattee86) based upon the semantic closure17 which is at the base of what we call the semiotic dimension of cognition. Without it, knowledge of (results of) perturbations or events would be indistinguishable from the (experience of these) perturbations themselves, and likewise there would be no need for representations, selectively identifiable from memory as a result of (temporally and/or locally) remote (knowledge of) experienced events.
It should also be noted that the correspondence between the system theoretical input-output relation and the object-percept relation as resulting from cognitive processing, is due to multiple processing loops which incrementally establish the similitude that allows for that analogy to be drawn. However, it is only by the concomitant separation of the system's processing in two interlocked feed-back loops, a) by processing input which results in states of perception of the object structure, and b) in processing these states which result in the output percept structure, that the distinction of processes of adaptation from processes of learning are reasonable. Thus, relating object input and percept output, cognition can be understood as an incremental learning process of constraint based information feedback which approximates object and percept structures under operational restrictions that the system's internal and the environment's external organization determine.
The transformation from a flow of perturbations (input) to the perception of an environmental object structure appears to be a consequence of and dependent on the system's processing capabilities rather than a feature solely based on the environmental conditions external to the system. The notion of grounded or embodied cognition accounts for this transformation by the definition of general constraints for the measurement of environmental perturbations and the representation of its results assumed to hold for all types of situated (cognitive) information processing. It may be characterized in a rough and informal way by the two feedback loops (a) and (b) (Fig. 2) of interlocked information processing in the system:
To bring home this point, cognition can well be characterized as knowledge based and memory dependent. This implies, however, that knowledge may also be represented in other than symbolic structures, and that memory need not be a separable module but can also consist of the system's state changes. Giving up the pre-established boundary between real-world objects and their system-dependent perception as symbol based mediation fostered by realistic models of cognition, and substituting it by processes which relate system and environment as their mutual situatedness, opens up a modeling perspective which allows to account for (some of) the cognitive complexities that language understanding still presents. In procedural models18 such processes can be devised to produce computable results whose visualizations - either based upon a system's internal state changes or its memory module structure and organization, or both - may converge on an endo/exo-distinction that is the result rather than the presupposition of cognitive processing.
Originally introduced as the pragmatic dimension in general semiotics, the notion of situatedness focuses on the relatedness of system, environment, and the processing concerned. It characterizes in an abstracting way the conditions that mutually constitute the restrictions on what (of the environment) can how (by the system) be realized or experienced. More specifically, the system's dependency on the knowledge of constraints as mediated by its awareness or the system's attunement, is complemented by the structural organization responsible for the system's immediate perception of environmental conditions constituting its adaptation. Both, attunement and adaptation19 are thus conditional for the systems' optimized performance (and/or long term survival20). They can be assumed to hold for all information processing in (natural/artificial) living systems in the sense that cognitive processing cannot be abstracted and freed from its situatedness (cite Bateson79).
The generality of situatedness and its grounding quality for cognitive language information processing systems to structure reality led semanticists to adopt this notion as fundamental. In model theoretic semantics it serves to allow for a communication based formal treatment of natural language meaning (cite BarwisePerry83, Devlin91) and possible applications (cite BarwiseGPT91, CooperMP90). What in the sequel we shall refer to as situation semantics theory (SST) is concerned with the development of a theory of information content or situated logic (cite Devlin90) which accounts for the constraints that contextual (i.e. situational or pragmatic) features of information processing produce. These constraints comply with the assumption, that beside spatial extension and temporal duration, it is the fundamental relatedness of situations whose regularities - whether or not these have been tacitly implied, explicitly included, or even parameterized in a model - trigger the signaling function for data to be identified as relevant for processing by an information system embedded in its environment.
The agent-relative framework that 'picks-out' the ontology is referred to as the scheme of individuation ... That is to say, in our study of activity (both physical and cognitive) of a particular agent or species of agent, we notice that there are certain regularities or uniformities that the agent either individuates or discriminates in his behavior. For instance, people individuate certain parts of reality as objects ('individuals' in our theory), and their behavior can vary in a systematic way according to spatial location, time, and the nature of the immediate environment (the 'situation type' in our theory). (cite[p. 81] Devlin90)In a realistic perspective, this view of situatedness makes the concept of infon - which is meant to denote a basic and abstract item of information21 - carry the coincidental burden of being both, independent of an information system and constituted by its processing. Evading this contradictory conception, our notion of situatedness can be understood instead as a direct consequence of life and living systems (cite Pattee89) accounting for their being-in-the-world22 that underlies - bar none - any process of cognition. As these situated processes can hopefully be accounted for by an (implementable) type of procedural model that realizes such processes rather than abstract and represent components of them symbolically for subsequent (rule-based) manipulation as in model theory, the concept of infons can be dispensed with in exchange for an elaborated concept of situatedness which allows to locate adaptation and attunement.
The particular forms of cognitive processing which deal with a segment of real-world structures that cannot sufficiently be characterized by their inter-subjective observability or their extension in space and time alone, have to be accommodated in system theoretical terms. When such bivalent entities like signs come into focus, the cognitive processes concerned which have been identified to constitute the SE relation of situatedness above (Fig. 2), discriminate clearly between such entities' immediate perception as evolving real world objects, and their mediate understanding as signs (like natural language structures) (re)presenting something else, which renders the cognitive processes semiotic. The distinction concerns the quality or function these entities have beyond their immediate perceptibility as real-world objects which can be modeled accordingly. In addition to and depending on that immediacy, however, these entities have (or acquire) a function which discriminates them and - due to their situatedness together with the system's concerned adaptation and attunement - transcends their immediacy or object structure. This function enables them to present and (re)present some entity of different ontological value as its mediation23. Whereas most objects have some functions in situations anyway, signs apparently owe their existence and observable space-time extension solely their obligation to enable inter-subjective mediation, i.e. to transcend their factual object character in order to constitute something we call meaning whose modus of processing is understanding24. Corresponding to this two-level ontology of signs is the system-environment relation being composed of the two interlocked situational cycles of processing (Fig. 3). While cognitive information processing is concerned with the observability of natural language discourse analogous to the knowledge based evolution of object structures from a flow of environmental perturbations (a), semiotic cognitive information processing is concerned with the constitution of meaning analogous to the knowledge based evolution of percept structures from a flow of natural language signs whose semantic values are direct (re)presentations of system-environment constraints as semantic space structure (b).
Considering the system-environment relation, virtuality may generally be characterized by the fact that it dispenses with the identity of space-time coordinates for system-environment pairs which normally prevails for this relation when qualified to be indexed real. It appears, that the dispensation of this identity - for short: space-time-dispensation - is not only conditional for the possible distinction of systems (mutually and relatively independent) from their environments, but also establishes a notion of representation which may be specified as exactly that part of a time-scaled process that can be separated and identified as its outcome or result in being (or becoming) part of another time-scale''.25 (cite[p.163] Rieg01)Accordingly, immediate or space-time-identical system-environments without intermediate representational form may well be distinguished from mediate or space-time-suspended system-environments whose particular representational import (as in NL texts) corresponds to their particular bivalent timely status both, as long-term types (composed of language signs whose feature to have understandable meaning is not directly observable), and as short-term tokens (directly observable and in need of being (re)cognized in order to be understood)26. This double identity calls for a particular modus of actualization (understanding) that may be characterized for systems appropriately adapted and attuned to such virtual environments. Actualization consists essentially in a twofold embedding to realize
In a (re)constructive stance of cognitive modeling this is tantamount to find implementable procedures for a kind of cognitive information processing which is based on the system's intrinsic structuredness and at the same time tied to its perception of the extrinsic environment, both being subject to change. In this perspective, identification and interpretation of external structures can be conceived dynamically as a property of double feedback in ecological information processing which (natural or artificial) systems - due to their own structuredness - are (or ought to be) able to perform: processing information which is cognitive as being based on knowledge structures, and dynamic as these structures get modified by processing constituting learning.
Semiotics as the general theory of signs goes back to Charles Sanders Peirce (1839-1924) who laid the foundations in his philosophical and theoretical writings (cite Peirce31) on the triadic ontology (1st-, 2nd- and 3rd-ness) of signs and their communicative use in the latter's functional trias (index, icon, symbol). The three dimensional theory of signs (cite Morris38) (syntactics, semantics, pragmatics) is commonly tied to Charles William Morris (1901-1979) who inspired the more descriptive and empirical development of semiotics since the thirties of the last century, resulting in the multitude of directions in contemporary semiotic study since. Ferdinand de Saussure (1857-1913), may be credited with the introduction of an holistic notion to the study of signs and languages (cite Saussure16) claiming that - particularly for linguistics as part of semiotics (sémiologie) - all language analysis ought to be directed towards the identification of the systematic relatedness of functions of language structures (langue) rather than towards signs and structures in isolation. Abstracted from and based upon regularities observable in the formation of signs and sign aggregates, the system underlying all natural languages appears to be constituted by an elementary two-level relatedness of linear syntagmatic order (syntagmes) and selective paradigmatic grouping (associations) of signs and strings of signs in recurrent cotexts27 of performative language use (parole). These findings - though later refined and in turn modified - proved to be fundamental for the structural paradigm in modern linguistics since.
Following the semiotic paradigm in natural language semantics as postulated decades ago (cite Rieg77d) can make a whole range of phenomena subject to linguistic investigation which - like vagueness and variability, adaptivity and dynamics, learnability and emergence of meaning - had been (and for some semanticists still are) excluded from the scope of linguistic enquiry and its focus of interest. For generative and unification-based grammatical approaches to natural language phenomena, as for philosophically motivated logical analyses within model-theoretic approaches to natural language meaning, the predominant study of language consists in the rule-based identification of structures and the symbol-based manipulation of their representations. Thus, truth-functional explication of linguistic constructs as abstracted from language discourse and represented symbolically by formal language expressions, have long outclassed and overshadowed any advances in numerical, subsymbolic, pattern-based, and perception-oriented approaches to natural language analysis.
Only recently have procedural models in computational semiotics (CS) succeeded in devising some functional (re)construction of implementable processes of meaning constitution. They have come up with computational means to simulate - or even realize28 - in software systems the way how meaning might be understood. Natural (and artificial) cognitive systems endowed with such processing capabilities which seem to be responsible not only for the understanding of language signs as meaningful, but also for the constitution of meaning as a form of inner/outer mediation, can well be identified as semiotic. Any semiotic cognitive information processing (SCIP) system, therefore, will have to be modeled as being capable of meaning constitution/understanding from processing natural language discourse whose results may be studied - as it were empirically, albeit indirectly - via implementations of algorithmized procedures and the structures they produce in an observable and controlled way.
It has been shown elsewhere (cite Rieg95b, Rieg95c, Rieg96a, Rieg99c) that an experimental setting based upon the quantitative analyses of structures of natural language discourse can offer some exceptionally seminal insights into SCIP system performance. This is due to the fact that collections of pragmatically homogeneous texts (PHT-corpora29) provide sufficient structural information whose relational constraints of linguistic structures and what they stand for can very effectively be exploited on that corporate level (cite Rieg77b, Rieg91c, Mehler01).
Text-based quantitative analyses of PHT corpora suggest and allow to develop procedural models for cognitive processes of language understanding. These employ reconstructive means other than in traditional linguistic approaches. While the latter are propositional in scope, focusing on linguistic structures up to the sentence level whose syntactically correct and semantically true formal reconstructions of typified phrase structure and sentence formation is considered a prerequisite to language understanding, the former approaches are based on structures other than and beyond the sentence boundary. They use procedures instead of categorial descriptions to define the entities in models that enact rather than describe processes of self-organization believed to underlie language understanding. These processes generate as their result relational representations which qualify to be named semiotic because in artificial SCIP systems they can be made to function (very much) like conceptual structures or internal models (see pp. pageref) as hypothesized by cognitive science for natural and artificial CLIP systems.
The dynamics of SCIP models depends essentially on their format of non-symbolic, distributed representations whose processing allow new representations to emerge as a multi-leveled form of self-organization. These emergent representations are tying the system to those segments of the real world which the language expressions are a part of and - when processed properly - convey information about as SE relations or their meanings. They do so both, according to their grammaticality and propositional contents external to the system in the above specified sense, a n d according to the system's own or internal understanding which can be learned from the non-propositional, syntagmatic and paradigmatic regularities in textual structures and may be visualized accordingly30. This is achieved by formalizing these SE ties not as functions abstracted from grammatical rules that are represented symbolically, but as a class of restrictions that are typified by (soft) constraints, modeled as procedures that produce (fuzzy) relations represented as (type-value) distributions. Resulting from computation, these are not another instance of transformed data representation but a new type of structural representation associating emergent entities (concepts) with observable entities (objects/signs) to realize what may be named understanding. The typified (soft) constraints are instantiated by procedures which operate on labeled linguistic structures and even allow to combine, mediate, and unify traditional (crisp) strata of cognitive investigation and categorial linguistic language analysis. It is the semiotic shift of perspective which thus replaces, or rather, complements formal definitions of symbolically represented (linguistic) entities by computable processes which make these (and other) entities emerge from structured (language) data as constrained (fuzzy) relations represented accordingly, without any other definition than the procedures which generate them. This procedural paradigm justifies to subsume such modeling approaches to natural language understanding under the name of computational semiotics.
These types of constraints appear to be general enough to be imposed contingently both, on material forms of observable entities (e.g. sign structures), and on particular settings in which these entities are observed (e.g. situation structures). Thus, (linguistic) entity and structure formation as well as (semiotic) sign and symbol function may be reconstructed as the two aspects of one type of process, constituting and at the same time acquiring syntagmatic constraints on linear agglomeration, and paradigmatic constraints on selectional choice of elements in natural language discourse. This is an extension to traditional linguistic analyses which have long - however coarsely - identified and represented their findings as morpho-phonemic, lexico-semantic, phraseo-syntactic and situational or pragma-semantic types of structures. In fuzzy linguistics32 (FL) these regularities may now be exploited at a much finer grain and represented in higher and dynamically adapting resolutions by text analyzing algorithms operating on different levels of structuredness33. Ideally, these algorithms accept natural language discourse as input and produce - via intermediate levels of (not necessarily symbolic) representations - interpretable structures of consistent regularities as output. Whereas the intermediate representations on different levels may be understood as the semiotic system's (hidden) layers of information processing, the system's own (internal) structuredness - which may (in parts) be visualized diagramatically - would represent its state of adaptation to the (external) structures of its environment as perceived and mediated by the natural language discourse processed.
Thus, semiotic cognitive information processing (SCIP) can be defined as the situated cognitive processing of information by humans and/or machines. Its semioticity consists in the multi-level representational performance of dynamic (working) structures underlying, emerging from, and at the same time being modified by such processing. It simultaneously constitutes meaning by exploiting constraints that are interpretable for properly attuned SCIP systems (cite Rieg01).
In information systems theory, situated SE relations (comprising system, environment, and processing) are considered cognitive inasmuch as the system's internal (formal and procedural) knowledge applied to identify and recognize structures external to the system is derived from former processes of environmental structure identification and interpretation. Situated cognitive SE relations become semiotic whenever this knowledge applied to recognize and interpret structured entities is based on or directed to object structures which are (representations of) results of self-organizing interlocked feedback processes through different levels of (inter-)mediate representation and/or emerging structuredness. This may be illustrated by the complexities of natural languages due to the double ontology of signs and symbols as aggregated - both syntagmatically and paradigmatically - in situated discourse.
According to Situation Semantics (cite BarwisePerry83) any natural language expression is tied to reality in two ways: by the discourse situation allowing an expression's meaning being interpreted and by the described situation allowing its interpretation being evaluated truth-functionally. In systems theoretical terms, this translates to meaning as the derivative of information processing which (natural or artificial) systems - due to their own structuredness - perform by recognizing similarities or invariants between situations that structure their surrounding environments (or fragments thereof). By ascertaining these invariants and by mapping them as uniformities across situations, cognitive systems properly attuned to them are able to identify and understand those bits of information which appear to be essential to form these systems' particular views of reality: a flow of types of situations related by uniformities like e.g. individuals, relations, and time-space-locations, and represented accordingly. These uniformities constrain a system's external world to become its view of reality as a specific fragment of persistent (and remembered) courses of events whose expectability (by their repetitiveness) renders them interpretable or even objective.
For SCIP systems, such uniformities appear to be signaled by natural language sign-types whose employment as sign-tokens in texts exhibit a form of structurally conditioned constraints. Taking the entity word as a componential example for semiotic sign structures, then these words and the way they are used by the speakers/hearers in discourse do not only allow to convey/understand meanings differently in different discourse situations (efficiency), but at the same time the discourses' total vocabulary and word usages also provide an empirically accessible basis for the analysis of structural (as opposed to referential) aspects of event-types and how these are related by virtue of word uniformities across phrases, sentences, and texts employed. Thus, as a means for the intensional characterization (as opposed to the extensional description) which constitute the situatedness of mediated SE relations by way of NL discourse, the regularities of word-usages serve as an access to and a representational format for those elastic constraints which underlie and condition any word-type's meaning, the interpretations it allows within possible contexts of use, and the information its actual word-token employment on a particular occasion may convey.
Moreover, in accord with Peirce's characterization of semiosis as a triadic relation35 , the SCIP systems' view allows to integrate different ontological abstractions of language
Although language philosophy and logics, information science and artificial intelligence, psychology and linguistics, and many other cognitive science disciplines (cite RatschStamatescu98) have attempted to contribute, unraveling (at least some of) the complexities inherent in the phenomenon of cognition under recourse to propositional language structures, it may be more promising to investigate, inversely, what the perception-based analysis of structures of performative language use - other than their propositional analyses - might contribute to the understanding of the role cognition plays in modeling language understanding. Such a (hopefully more adequate) model could allow for experimental tests of its results of (non-propositional) understanding of texts against the observable structures of the real world as described by true propositions expressed in natural language sentences from these texts. As both these (world and language) structures have spurred interdisciplinary hypothesizing for some time now, the (overt and hidden) functions which aggregates of language signs (words, phrases, sentences, texts, etc.) in discourse exhibit, are far from being well understood yet. In the course of research, only a few were (partly) identified and analyzed, their conditions examined, and their possibilities determined as to what extent they can - in a general and abstract way - be characterized as constraints allowing these functions to serve their purposes the way they do.
Following a systems theoretical view (see pp. ) which allows to distinguish cognitive processing of environmental stimuli as immediate (signal) perception, from those resulting in mediated (sign/symbol) understanding, reveals that the highly functional and optimized constraints which are realized by language structures and instantiated in communicative discourse, enable a cognitive system to replace its (immediate) entity-observer relatedness of signal-based cognition by a (mediated) representation of it, or rather - to be more precise - by the sign/symbol based mediation of cognitive results that might (but need not) stem from immediate perception (or its derivatives)38. In establishing this (mediate) sign-interpreter or language-understander relation, a very particular situation is invoked which renders co- and contextual constraints effective that relax the cognitive system's dependence on primal observation and experience of environmental conditions which confine the immediacy of perception of language signs (and aggregates thereof). This relaxation, however, works only at the price of situatedness39 which comprises the knowledge of both, the signs' presentational means that come as a cognitive system's awareness of or attunement40 to these constraints, and the signs' representational import which comes as a cognitive system's grounding41 as being part of and embedded into the interaction with its environment, and makes (some) objects signs and their modus of perception understanding. Although all this semiotic knowledge has to be acquired somehow by experiential, attuned, situational, and grounded performance in order to be stored retrievably before becoming effective, this price has proved to be good value regarding the apparent (ontogenetical) superiority to other species' means of (phylogenetical) knowledge acquisition and transmission42 which natural (and formal) languages and their mediating potential brought about for individuals, human society, and mankind.
Therefore, the focus of our investigation is on the tie that hooks certain physical objects to other physical objects which due to specific (co- and contextual) conditions acquire different ontological status (physical objects become signs) allowing to distinguish language elements z Î V and what they mean, stand for or represent in the universe of discourse x Î U. This tie is realized by natural languages L which can formally be defined - based upon fuzzy set theory (FST) (cite Zadeh65) - as a relation (not a function) L=V×U that is general enough to allow for more than binary or crisp membership (z,x) Î L. According to Zadeh (cite[p.168] Zadeh71) it can be characterized by the membership function
Defined in accord with realistic semantic theory for aggregates T of language signs from the vocabulary zi Î T Í V and collections X of entities in the universe of discourse xk Î X Ì U, this two-way correspondence of m L (Eqn. 1) allows for a formal declaration of (natural) language meaning M
Trying to apply these formula in praxi, however, is to encounter severe difficulties. In general, neither V and U nor mL are known in their entirety, and only fragments of natural languages and of the universe are empirically accessible whose partly determined structures scarcely compensate for this lack. Also, numerical coefficients are yet to be found for the computation of membership values in (2) and (3) in a theoretically well founded way of NL reference semantics. These would allow to replace the (more or less) ad hoc and/or subjective estimates which so far prevail in representations of Mz and Mx, by testable algorithms or operations that could empirically be evaluated. Although Zadeh's fuzzy referential models of NL meaning like Possibilistic Relational Universal Fuzzy (PRUF) (cite Zadeh78) and TestScore Semantics (TSS) (cite Zadeh81) are plausible and can indeed claim to have realized an operational working hypotheses (cite Rieg01a), these and later developments do not yet provide a general solution that can be algorithmized and applied in processes of meaning constitution (i.e. understanding) by machine.
Earlier applications of FST to linguistic and NL semantics (cite Rieg74) had produced some evidence that R(z) and D(x) could not be assumed to be directly measurable or computable form texts. Therefore, the reconstruction of linguistic meaning relations was proposed (cite Rieg79a) suggesting an empirical analysis of structural language constraints and their formal reconstruction as compositions of fuzzy relations. For these, numerical coefficients could be devised with computable algorithms for the electronic processing of masses of natural language texts which began to become available since the late seventies providing the necessary amounts of accessible data for statistical analyses (cite Rieg81d).
The first level is concerned with the formal reconstruction of reference and description. As shown in the diagram of morphisms (Fig. 5), for all zi Î T Í V and xk Î X Ì U by way of p Î M Í I, as well as for all xk Î X Ì U and zi Î T Í V by way of e Î E Í G respectively, the following compositions can be declared
The diagram (Fig. 5) can also reveal how the relatedness of different ontologies (of data material and of real world objects) may have lead cognitive psychology and cognitive linguistics to an unwarranted merge of formats for M and G creating the notion of linguistic transparency44 for cognitive models which rather amounts to the opposite. Instead, the declaration of granular meaning relations and their resulting systems (of sets of fuzzy subsets) attempts to account for the ontological difference of cognitive processes underlying description as the intended (re)presentation of real world entities produced by NL expressions, as opposed to understanding as the perception of symbol aggregates and the constitution of what they convey or stand for. This distinction of processes of meaning constitution from those of NL discourse generation is based on related inter-mediate (re)presentations of not only
Thus, understanding a language L introduced (Fig. 4) as a two-way meaning relation M:T« X (Eqn. 4) of reference (Eqn. 5) and of description (Eqn. 7) has been dissolved by the intermediate representations of intensions M Í I and grammar E Í G respectively. Together with the real world entities X Ì U and the NL expressions T Í V, these allow also for the dissolution of the two-way relation T« X into a cycle of mappings comprising V® I® U®G® V whose (hopefully) implementable instanciations
So far, this cycle only seems to corroborate what cognitive linguists have hypothesized about natural language processing, as being dependent on different types of knowledge of which linguistic knowledge (i.e. E Í G as formalized by grammars) and real world knowledge (i.e. M Í I as represented in mental models) are the most prominent. However, cast into the mould of morphisms which relate them, this re-formulation (Fig. 5 and Eqn. 9) not only allows for the dynamism in NL understanding to be represented accordingly in a formal way. Instead, it also provides some - as yet formally specified - hints as to how, why, and by what means these knowledge bases might (have to) be augmented, complemented, or altogether substituted in the desire to translate this formal model's morphisms into empirically testable operations which parameterize relations, restrictions, functions, etc. and generate emergent representations as their result.
The second level of granular decomposition is a consequence of having refuted linguistic transparency45 as an obliging exigency for cognitive modeling on phenomenological grounds. Since we have postulated different types of intermediate structures as declared above - (non propositional) intensions like M Í I as opposed to (linguistic) grammars like E Ì G - these are in want of representational formats and/or operational specification extending the morphisms devised so far (Fig. 5). For formal grammars G, this requirement is easily met considering the numerous types of different NL grammars which have been developed, implemented, tested, and evaluated in computational linguistics (CL) during the last three decades. Looking for operational approaches to reconstruct intensions I satisfying similar conditions of empirical, preferably algorithmic analysis and formal representation of conceptual structures, their organization and processing, is less successful. Most of the research and development advanced by cognitive psychology (CP) and cognitive linguistics has to be discarded due to their models' lacking generality and/or limited applicability that goes with the propositional format of symbolic representations they adhere to. Therefore, the second stage in the formal reconstruction of relatedness has to somehow enable the instanciation of the two morphisms devised so far, namely designation and denotation (Eqn. 5 and Fig. 5) for which the tool of granular decomposition - as employed at the first level above - can again be applied (Fig. 6) with the advantage of ready to be used models being available for both.
The designation relation des Í T×M is covered by a model of meaning analysis and representation in structural NL semantics. Conceived as a two-level text analyzing process recursively applied to PHT corpora as input, this model (cite Rieg89) produces a multi-resolutional representational system (of sets of fuzzy subsets) as output of vector formatted meaning representations in semantic hyperspace (SHS). It can be interpreted as the (fuzzy) intensional structure resulting from the algorithmized processing of NL texts. The underlying procedure presupposes neither prior world' knowledge of the universe (in whatever symbolic format), nor any linguistic' knowledge of the syntax and semantics (as provided by whatever grammar formalism). Thus, the vector formatted representations emerging from the analyzing process of the SHS model can serve as an instanciation of the designation relation, i.e. of how a system (of structured sets of fuzzy subsets) of abstract but linguistically labeled entities (intensions) may be derived from language patterns automatically recognized. These are not only part of the (empirically) observable reality (situated language material) but also a condition for understandable language meanings (grounded informational contents) due to the constraints that semiotic processing constitutes (i.e. defines and makes use of) between different descriptive levels of linguistic structures46 in particular.
As for the denotation relation den Í M×X, there is also a candidate available in situation (semantics) theory (SST) (cite Devlin91) which will allow to reconstruct this morphism from representations of intensions to what they may denote in the universe of discourse. Other than in more traditional theories of realistic semantics, the founding concept of situatedness allows to account for reality in a way which does not merely identify the formal expressions of symbolic representations with the real world entity they are meant to stand for47. An ontologically more adequate treatment is achieved by intermediate levels of granular representations that distinguish real situations from abstract ones mediated by situational uniformities common to both. As typified by SST, real situations are no sets any more but parts of reality which provide the experiential foundations of (and hence are ontologically prior to) all subsequent abstractions that will characterize them. These abstractions are called uniformities represented by abstract entities like individuals, relations, spatial/temporal locations, etc. that tie situations together and allow for the derivation of abstract situations which classify real situations of system-environment (SE) relatedness. Although not (yet) algorithmized, SST provides the formalisms for assigning intensional representations to real world entities in the universe.
In Fig. 6 as the extended model of morphisms, both, SHS and SST serve their purpose by intermediate representations (as corpus space C and as system of situational uniformities S) that can either algorithmically be computed (like C for des) or generally be derived (like S for den) which may be introduced as follows.
For the SHS model, universal constraints of NL language structure formation known as syntagmatics and paradigmatics have been operationalized whose formal declaration as consecutive mappings is but a set theoretical composition of these two relations. As shown in the corresponding diagram of morphisms (Fig. 6), for all zi Î T Í V and pj Î M Í I the intermediate representation is y Î C and allows to formally define the following composition
Based upon the first cycle (Eqn. 9), the new compositions above determine another, extended cycle comprising V® C® I® S® U®G® V whose implementable instanciations
By these explicit declarations, a formal framework is laid not only for the theoretical but also for the empirical reconstruction. So-called semiotic procedures will have to be found that instantiate these morphisms48 (and partial relations) to model the process of meaning constitution from observable language structures to result in interpretable representations of what they convey as their informational contents.
Structural linguistics (cite Saussure16) has contributed substantially to how language items come about to be employed in communicative discourse the way they are. Fundamental for structural linguistics is the identification of universal49 constraints underlying natural languages and their observable structures. These constraints control the multi-level combinability and formation of language entities based upon the distinction of restrictions on linear aggregation of elements (syntagmatics ) from restrictions on their selective replacement (paradigmatics ). It is these two-level constraints that fuzzy linguistics has succeeded to operationalize by devising computable procedures (cite Rieg95a) for which algorithms have been found that instantiate them, detect and analyze language regularities, and exploit observable structures produced by the constraints concerned (cite Rieg97a).
Control constraints or mechanisms are, of course, a very complicated and ill-defined set of structures. But in essence control implies that a system possesses alternative behaviors, and that owing to the particular nature of the constraint it is possible to correlate a controlling input variable or signal with a particular alternative output dynamics according to a rule [or rather, regularity]. Again it is important to realize that controls must operate between different descriptive levels, just as constraints must be defined by different descriptive levels. This is necessarily the case for all [...] informational processes in which a number of alternatives on one level of description is reduced by some evaluative procedure at a higher level of description.'' (cite[p.251, my italics] Pattee72)Thus, to describe regularities by computational procedures is not only to measure varying degrees of combinatorial determinacy and to detect different patterns of the language elements' and structures' linear distributions (in texts) but also to represent their values as labeled possibility distributions. Such procedures may therefore be identified with the regularities they are able to detect as constraints. Being applied recursively to huge amounts of NL data in PHT corpora, the constraints structuring them will be represented as vectors in possibility spaces from which observable syntagmata and paradigmata can be computed.
The basically descriptive statistics used to grasp these fuzzy relations on the level of words in discourse are centered around a measure of correlation (Eqn. 15) to specify intensities of co-occurring lexical items in texts, and a measure of similarity (or rather, dissimilarity) (Eqn. 18) to specify these correlational value distributions' differences. Simultaneously, these measures may also be interpreted semiotically as instantiating the composition of syn and par (Eqn. 11) as set theoretical constraints or formal mappings (Eqs. 16 and 19) which model the meanings of words as a function of all differences of all usage regularities detected for a vocabulary as employed in a PHT corpus.
For such a corpus K={ kt } which consists of texts t=1,¼,T of overall length L=åt=1Tlt with 1 £ lt £ L, measured by the number of word-tokens per text from a vocabulary V={ zn }; n=1,¼,i,j,¼m of m word-types zn of different identity i,j whose frequencies are denoted by Hi=åt=1Thit; 0 £ hit £ Hi, the modified correlation coefficient ai,j (Eqn. 15) allows to measure for all n word types their pairwise relatedness (zi,zj) Î V ×V by numerical values ranging from -1 to +1 by calculating co-occurring frequencies of tokens in the following way
Evidently, pairs of items which frequently either co-occur in, or are both absent from, a number of texts will positively be correlated and hence called affined, those of which only one (and not the other) frequently occurs in a number of texts will negatively be correlated and hence called repugnant.
As a fuzzy binary relation, a: V×V®Áa can be conditioned on any zn Î V which yields a crisp mapping as operational definition of the syn relation
As shown in Tab. 1, the regularities of usages of each lexical item can numerically be expressed by the a-tuples of affinity/repugnancy -values measured against any other item of the vocabulary V×V as employed in the text corpus analyzed. By a-abstraction each m-tuple of a-values (rows) defines an element - the so-called corpus point - yi Î C in the system C (the set of fuzzy subsets of the vocabulary) represented as vectors in the corpus space which is spanned by the number m of axes each corresponding to one vocabulary entry.
And as shown in Tab. 1, the differences of usage regularities of lexical items C×C are calculated and numerically expressed by d-values whose similarity/dissimilarity form the base of d-abstraction. The resulting d-tuples of each one corpus point measured against all the others in the system (corpus space) define and identify new abstract entities in a new system, i.e. meaning points pn Î M. After introducing a Euclidian metric z: M ×M® \mathbbR , its labeled elements may again be measured to specify fuzzy subsets of potential paradigms which can structurally be constrained and evaluated without (direct or indirect) recourse to any pre-existent external world. By
Essentially, these new representational structures are value distributions or vectors of input entities that depict properties of their structural relatedness, constituting multi-dimensional systems and (metric) space structures (semiotic spaces ). Their elements may be interpreted in a variety of ways as (labeled) fuzzy sets allowing set theoretical and numerical operations be exercised on these representations that do not require categorial type (crisp ) definitions of concept formations, or as entities (points) in space structures allowing topological interpretations and the procedural definition of new (dynamic) organizations generated by algorithms which operate on such spaces and reorganize their structure in dependency graphs (cite Rieg85c) according to any chosen point's perspective (cite Rieg01).
To give an idea of how this grounding (see p. pageref) is assumed to be modeled for the reconstructive purpose at hand, lets think of the phenomenon of dynamics observable in the real world or the universe as a function of spatiality and temporality. Although these concepts are indistinguishable at the genotypical source, they ought to be realized as discriminating both systems from environments by extending into higher complexities. In Fig. 8 this source point is marked by a circle from which the concept types of spatiality, temporality, and their mutual composite dynamics extend to (a plane of) their increasing distinguishability (vectorially illustrated by arrows), as do the concepts of system and its environment (orthogonal to that plane) determining the spaces above and below (that plane) which are conditional for the notion of dynamics and its observable (operational, measurable, etc.) accessibility.
For terminological clarity, the scaling of the spatial, temporal, and dynamic arrows extending from the source point can - tentatively as in Fig. 8 - be instantiated by concepts whose parameterizations differ - not only by name - for the system area (above the plane) and the environment area (below the plane), allowing to capture the duality which is the only view that realistic epistemology provide. Thus, dynamics translates for systems to their mobility which may be characterized by pace step per endo-time cycle ratio, whereas for environments the dynamics amounts to their variation measured by grid number per exo-time cycle ratio51. Satisfying certain conditions of monotonicity, a system's mobility may further be specified by the direction of its moves, and the environmental variation by the orientation of its changes52. To characterize the system-environment relatedness of situated cognitive processes, instanciations of types of parameters like pace/grid, direction/orientation, endo/exo-time - and many more that might be specified for different situations of arbitrary complexity - not only have to be identified but also are to be determined in how they couple systems and environments structurally to each other.
For SCIP system-environments (as specified for experimental test purposes in Tabs. and below), this coupling can be determined by the isomorphism of system directions and environment orientations D=O, and the correspondence of pace and grid as a function f(P/G), whereas - for reasons of simplicity - temporal coupling was neglected altogether as a modeling parameter. Hence, mobility is modeled as the system's moving about at a pace-grid ratio k/g from system position SPP to system position SPP+1 for all R(n0,m0) Î ÂP in the reference plane where (fixed) object locations OLR(n,m) mark those grid points that cannot be taken or moved to by the system. Thus, relations of system positions and object locations (SPOL-relations) are what couples the cognitive system with its environment. This SE relation, however, is not experienced directly by the system as measured by changing coordinate values for its moving positions in the universe, but rather mediated by natural language descriptions of that relation whose situational processing constitutes (understanding of) its meaning and serves as - what might be called - a semiotic or SCIP coupling.
This rather rough approximation of very simple situational uniformities which would likely be identified to determine equally simple relations of cognitive systems within their environments, is to illustrate which minimal requirements a SCIP situation of system-environment relatedness will have to satisfy. In order to let intensional representations p Î M Í I from processing NL discourse be assigned to real world entities x Î X Ì U in the universe, these requirements, or rather some (gradual) satisfaction of them, ground that system by way of its understanding of meanings mediated or described by the textual structures in the discourse processed. In fact, presupposing the informational meaningfulness of discourse (instead of the existence of the real world as environment and the cognitive mind/brain as system) will render PHT corpora to become representations of semiotic SE situations.
Processing SCIP coupled natural language PHT corpora the way which the morphisms (Fig. 6) and their instanciations indicate, would appear to grasp some relevant portions of the ability of language understanding. Whenever a system - processing language regularities in z Î T Í V that are external to it - comes up with an internal representation of structure p Î P Í M which specifies the informational contents of what the corpus processed describes of the real world facts x Î X Ì U, then the system has enacted some learning. A semiotic cognitive information processing (SCIP) system endowed with these capabilities and performing likewise in building up an internal representation of its processing results would consequently be said to have constituted some - however shallow - text understanding by the computations the procedural model specifies. This is what the first cycle of morphisms (Fig. 5 and Eqn. 9) and the processing of the SCIP system's situational setting (Fig. 3) are to illustrate in a formal and a schematic way. And this is also what the second cycle of morphisms (Fig. 6 and Eqn. 14) has been devised to determine formally in Tab. 1.
The problem that has to be addressed now is, whether (and if so, how) the contents of what such a system is said to have acquired or understood (processing PHT corpora) can be tested, i.e. made accessible for scrutiny other than by understanding these very texts, and without committing to a particular semantics whose presuppositions would inevitably determine all possible interpretations. What we have at our disposal so far, is a system of word meanings (lexical knowledge) which has been modeled in a vector space format áM,zñ as a relational data structure whose linguistically labeled elements (meaning points) and their mutual distances (meaning differences) form a system of potential stereotypes 53. Meaning representation via points (or vectors) in semantic hyper space (SHS) is a matter of the position a point (or the direction a vector) takes among others, and it is this position (or direction) in that system which interprets the lexical label attached to it, not vice versa (cite Rieg85a, Rieg85c). Therefore, based upon SHS-structure as computed from the items' usages in the discourse analyzed, the meaning of a lexical item may be described either as a fuzzy subset of the vocabulary, or as a meaning point's vector, or as a meaning point's topological environment delimiting the central point's position indirectly as its stereotype.
This variability of representational formats complies with the semiotic notion of understanding and meaning constitution according to which the SHS may be considered the core or base model of an artificial multi-level conceptual knowledge representation system (cite Rieg89). As we have separated cognitive processes from their resultant structures above, so may we distinguish here between the short-term process in a situational embedding (employment or activation) constituting the attuned system's adaptation, and its long-term structure as the addressable representation of knowledge (stereotype or concept) which is a form of learning54. From a semiotic point-of-view both are necessary components of understanding with the implication that the structures depend on the processes and vice versa to let addressable representations emerge and cognitive processes be enacted. Thus, the duality of the inner-outer distinction or the system-environment opposition may be mediated (or even suspended) by processes operating on some supposedly common, basal representational structures55 whose dynamics and efficient (re)organization is part of understanding and can thus only be modeled procedurally.
As we have introduced the process-result perspective on cognition to allow the mind-matter or endo-exo distinction become a result of cognitive processing rather than its presupposition, what appears to be disturbing on first sight is that the procedural models of cognitive processes - not the processes themselves - produce accessible results by their representational structures which - depending on the way they are addressed - will result in the (more or less subjective) internal or endo-view the system develops, a n d simultaneously in a (more or less objective) external or exo-view of the surrounding environment that constitutes the system's reality by virtue of its endo-structure56. However, on second thought the computational semiotician finds herself/himself engaged in a constitutive part of the very process of learning to understand or in constituting meaning (as a semiotic function) which she/he was trying to model as a process of knowledge-based information processing (as a cognitive function). Apparently, realizational models of semiotic aspects of cognition will produce emergent representational results which are open to perspectival (endo/exo ) interpretation whereas simulative models will not.
To find out (and preferably be able to test) what of the structural information inherent in natural language discourse - as defined a n d structured by the computational processes of textual analyses described above - might be involved in mediating or constituting that duality, an experimental setting has been designed. It is based on the assumption that a type of core structure - similar to that one modeled by SHS - ought to be postulated. This core could be considered a common base for different notions of meaning or content of natural language expressions developed by theories of referential and situational semantics as well as some theories of structural or stereotype meanings. Therefore, real world situations with directly and externally observable space-time parameters, however restricted, are to be preferred over any conceivable symbolic representation of such situations whose encoding might introduce unwarranted abstractions and/or simplifications.
To give a general view of the approach first, the experimental setting is imagined to consist of an artificial mobile system in a two dimensional environment with some objects at certain places which are to be identified57. The system's channels of perception allowing to form its own or endo- view of its surroundings are extremely limited, and its ability to act (and react) is heavily restricted compared to natural or living information processing systems. What makes such a software system a semiotic one is that - whatever it might gather from its environment - it will not be the result of some decoding processes which would necessarily call for that code to be known to the system. Instead, any result will be constituted according to the system's (co- and contextually restricted) susceptibility and processing capabilities to (re)organize the environmental data, i.e. natural language texts, a n d to (re)present the results in some dynamic structure which determines the system's knowledge (susceptibility), learning (change) and understanding (representation).
The experimental setting developed to allow for testing language understanding against the reality described without committing to the semiotically unwarranted presuppositions of sentencial and truth-conditional reconstructions of language processing, is still tentative. It hinges on the assumption that cognitive information processing will both operate on and produce structures as a condition for and/or a result of such processing. These structures have to have some space-time extension, i.e. are in principle observable apart from and independent of being processed cognitively. The processes operating on and modifying them can also in principle be dealt with independent of their temporal duration by procedures which can be defined as processes abstracted from their temporality. Procedures can be represented formally, their notational format be parsed and checked for correctness, their expressions be interpreted or compiled for execution and - provided a suitable automaton is available - become initial for the enactment of processes in time again, having not only a certain duration but also the effect of operating on and modifying structures which in fact - not only in principle - are observable as (input-output related) changes.
This two-sided independence facilitates procedural cognitive models to relate structured language expressions which can be analyzed (or observed) without being understood, to language understanding processes which can be conceived (as procedures) being abstracted from their temporal duration. It appears, that by this move procedures and algorithms found to model some aspects of cognitive information processing for language comprehension can be tested against - not on the grounds of - any other accepted, well defined model of cognitive (language) understanding. And test results would have to be considered (partially) positive for all cases in which the contents of the same language expressions is represented or depicted in identical (or at least similar) results for both models.
Thus, to enable an inter-subjective scrutiny, the (unknown) results of an abstract artificial SCIP system's (well known) processing of natural language discourse is tested against and compared to the (well known) interpretative results which linguistics proper and computational linguistics traditionally agree to propose for the (unknown) processes of natural language meaning constitution58. Accordingly, the propositional form of natural language predication will be used here only to control both the format and the contents of the natural language training material, not, however, to determine the way it is processed in modeling learning and language understanding.
In this way, the exo-knowledge which the experiment's designer has to control for the propositional encoding and decoding of information in texts that the SCIP system will be exposed to, can indeed be kept strictly apart from the system's endo- capacities of text processing which by definition do not include this knowledge. Thus, the system's own non-propositional processing will allow for some results as the system's internal representations which would not be interpretable as mere repetitious reproductions or as an application of knowledge structures made available to it externally. Instead, these endo-results would have in principle a chance to be different from - though hopefully comparable to - the exo-view of its environment as specified by propositional descriptions. This is tantamount to the quest for a representation whose format allows visualization of endo -computed adjacencies and comparison to exo -defined relations.
In the course of this visualization process - outlined in some detail elsewhere (cite[pp.157-193] Rieg01) and only summarized here - the composite morphisms (Fig. 7) as modeled in the two-level mapping of emergent abstractions (Tab. 1) result in áM,zñ or the semantic hyper space (SHS) whose intrinsic structuredness can be exploited in a three stage process:
The fuzziness of this image is quite remarkable in so far as it does not concern the object locations themselves but rather the referential space around them allowing for their differentiation as illustrated by its 3-dimensional profile (Fig. 11 1). This sort of holistic and indirect way of specification-as opposed to the direct by stating two coordinate values to determine a location-is self-including and organized around the entities to be specified. It does not, therefore, need (or rely on) any categorial presuppositions of how points may be defined exterior to the self-organizing process whose emergent results structure space in a way to allow it to become (potentially) referential . It should be noted here, however, that the initial format of visualization chosen to be a two-dimensional plane spanned by orthogonal coordinates is not a situational necessity of the space concept but only the most conventionalized frame for representing definite locations by abstracting from their situational embedding.
The strict separation of the computational processes from their results on the system's side now corresponds to the sharp distinction between the formal specification to control the propositional generation of descriptive language material and the factual situation of varying system positions relative to fixed object locations (SPOL-dynamics) of which - in all of its instances - the language material gives a referentially true description. As the language material is in both cases the medium of representation for objects located in the reference plane at certain places, it serves well as the postulated structural coupling for testing a SCIP system's performance to collect and represent referential information from discourse. The non-propositional processing of a set (corpus) of sets (texts) of correct language expressions (sentences) of true meanings (propositions) describing (fixed) object locations relative to (varying) system positions resulted in a (dynamic) topology of labeled meaning points. Being in a vector space format (SHS), its intrinsic structure was made visible by three consecutive stages of representations. These visualizations were based on the crisp 1.0 interpretations of the hedges. Using instead the fuzzy 1.1 definitions (Tab.6) to interpret the adjacencies of hedged core predicate labels has produced comparable images due to even more distinctive structures emerging from the data as outlined elsewhere (cite[pp.192] Rieg01).
It is worthwhile noting here again, that the SCIP system's processing is neither based on, nor does it involve any knowledge of syntax or semantics on the system's side (Tab. 3). Thus, the SHS structure appears to emerge from the system's NL text processing and representation procedures which realize learning as a procedural model of meaning constitution and knowledge acquisition enacted as (a sort of) perception based language understanding by machine.
As an object for the modeling enterprise, NL understanding is ambiguous: it applies likewise to the processes concerned as well as to their results whose mutual dependency has to be accounted for by models claiming to be adequate. Clarifying the process/result ambiguity is to analyze and to specify: analyze in order to find the type of structures underlying the results, and specify in order to determine the class of processes which will produce these results, before procedures can be devised whose implemented instanciations may qualify as realizing these processes which will operate on and, in turn, modify (old) and generate (new) structures as the results of NL understanding.
In accordance with the theory of information systems, functions like interpreting signs and understanding meanings translate to processes which extend the fragments of reality accessible to a living (natural and possibly artificial) cognitive system beyond reality's material manifestations. This extension was based on the distinction of immediate from mediate system-environment relations which allowed to characterize adaptation as a process of necessarily identical space-time coordinates for SE relations, as opposed to learning as a process with that identity suspended, but in need of memory to establish that relation. Natural language understanding is a process of meaning constitution based on both, adaptation and learning, and modeled and performed as enactive learning by semiotic cognitive information processing (SCIP) systems. These are grounded in the triadic procedures of semiosis (among sign, object and interpretant), and its two-fold situatedness (of discourse and description constraints) corresponding to the double ontology of language signals as (physical) objects and (cognitive) meanings.
1The author is indebted to Christoph Flores, Daniel John and Alexander Mehler for discussions, and to Michael M. Richter for valuable comments on some of the ideas expressed in this paper. As always, any errors are mine.
2 Science is based on observation, hence on the use of the senses. The problem is to eliminate the subjective features and to maintain only statements which can be confirmed by several individuals in an objective way [...] Science aims at a closer relation between word and fact. Its methods consists in finding correlations of one kind of subjective sense impressions with other kinds, using the one as indicators for the other, and in this way establishes what is called a fact of observation.'' (cite[p.33, my italics] Born64)
3 In particular, it is based on an experimental approach in which progress is made by performing experiments that can directly judge between competing scientific hypothesis about the nature of cognitive mechanisms. In most experiments situations are created in which the variety of actions is strictly controlled and only a very limited aspect of situation is considered relevant to the pattern of recurrence. [...] The assumption underlying this empirical research is that general laws can be found in these restricted cases that will apply (albeit in a more complex way) to a much broader spectrum of cognitive activity.'' (cite[pp. 24] WinogradFlores86)
4According to Simon: A physical symbol system holds a set of entities, called symbols. These are physical patterns (e.g. chalk marks on a blackboard) that can occur as components of symbol structures (sometimes called 'expressions'). [...] a symbol system also possesses a number of simple processes that operate upon symbol structures - processes that create, modify, copy, and destroy symbols. A physical symbol system is a machine that, as it moves through time, produces an evolving collection of symbol structures. Symbol structures can, and commonly do, serve as internal representations (e.g. 'mental images') of the environments to which the symbol system is seeking to adapt.'' (cite[p.27]Simon82)
5As emphasized nearly three decades ago by Pattee who identified the dependence of biological systems on physical constraints together with their ability of internal self-interpretation as being constitutive for symbol structures: And this interpretation is not a property of the single molecule, which is only a symbol vehicle, but a consequence of a coherent set of constraints with which they interact [...] raising the question of representation so] that the most fundamental concept of a constraint in physics depends on an alternative description, and that the apparent simplicity of constraints is in fact a property of the language in which it is described.'' (cite[pp. 248] Pattee72)
6The term is polysemous in English as it can likewise be understood as the adjectival form of language and of linguistics. To allow for a distinction of these two meanings which in some other languages have in fact been lexicalized (by providing different words), we will confine linguistic to designate properties of (theories, models, methods, concepts, etc. of) linguistics as the scientific discipline investigating natural languages, and language, language-like or performative to refer to those of (directly observable or experiential) language phenomena.
7This includes types of knowledge concerning the external world (e.g. common sense) and the sign systems employed (e.g. languages)
8As an object for the modeling enterprise, NL understanding is ambiguous: it applies likewise to the processes concerned as well as to their results whose mutual dependency has to be accounted for by adequate models. Clarifying the process/result ambiguity is to analyze and to specify: analyze in order to find the type of structures underlying the results, and to specify in order to determine the class of processes which will produce these results, before procedures can be devised whose implemented instanciations may qualify as realizing these processes which will operate on and, in turn, modify (old) and generate (new) structures as the results of NL understanding.
9 Empirical and procedural models serve their purpose by abstracting from irrelevant and by isolating relevant parts of the original, and by representing the interrelations, structures, functions, processes, etc. that characterize these parts in a format which allows repetition of processes, reproduction of results, and their inter-subjective scrutiny for concurrently forced agreement to its outcomes. Procedural and operational definitions of terms in experimental settings ensure the terms' employment in propositional expressions with space-time related falsification possibilities.
10 In broad terms, a mental model is to be understood as a dynamic symbolic representation of external objects or events on the part of some natural or artificial cognitive system.'' (cite[p. 9] RickheitSichel99)
11For a model of mediated interpretation, however, see Fig. 5, p. 72 below where a granular (set theoretical) decomposition is declared and a proper (relational) definition of designation, denotation, description, and reference is given as employed throughout this paper.
12Failing to combine the two branches of representational formats (rule-based, symbolic, declarative vs. pattern-based, numerical or subsymbolic, procedural) in knowledge representation and processing, will keep phenomena like adaptivity, creativity, dynamics, emergence, learnability, variability, vagueness, and self-organization outside the scope of what rule-based computing and symbol manipulation techniques have been able to achieve so far modeling automatic language processing (by way of grammar formalisms, sentence parsing techniques and generation, deduction and inferencing mechanisms). (cite[pp. 248] Rieg91a)
13According to Peirce, the three-way dependency he named semiosis of sign, object, and interpretant - as embodied in but not resolvable by relations like designation, denotation, or reference determining signs, intensions and extensions derived from Morris's semiotic trias - can only procedurally be enacted: by semiosis I mean [...] an action, or influence, which is, or involves, a coöperation of three subjects, such as sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs.'' (cite[p.282] Peirce06)
14Note, that the notion (and problem) of understanding does not occur anymore because the meaning of NL expressions had been - in Tarski an tradition (cite Tarski35) - either transformed (cite Tarski44) via displacement by formally defined truth functions and their (tabular) evaluation, or dissolved (cite Carnap55) via formal expressions of truth conditions encoding their informational content in symbols. Both, symbolic encoding and evaluation of truth, however, presuppose prior (embodied) understanding.
15A notable exception is again Situation Semantics: It is fairly common practice in mathematical semantics simply to identify the world with the structure that represents it. But this identification hides an important aspect of the whole endeavor, [...] This is why we explicitly distinguish real situations from abstract ones that accurately classify real situations.'' (cite[p. 57] BarwisePerry83)
16 The grounding problem is [...] of how to causally connect an artificial agent with its environment such that the agent's behaviour, as well as the mechanisms, representations, etc. underlying it, can be intrinsic and meaningful to itself, rather than dependent on an external designer or observer.'' (cite[p.177, my italics] Ziemke99)
17 The semantic closure principle allows us to treat the action of a measuring device as primitive because the details of its construction are accounted for by a [... representation], while the meaning of the [... representation] can be treated as primitive because the details of the interpretation are accounted for by a set of measuring devices.'' (cite[p.275] Pattee86)
18Roughly, these are models whose object entities essentially are represented as and defined by procedures. Other than symbolically represented propositions defining (crisp and/or soft) categories, procedures are formal notations of processes (abstracted from their timeliness) which can ideally be algorithmized in order to be implemented as programs to run in computers (in time again) and operate on data structures yielding results which alter these structures and hence may be observed as being changed in their (spatial and/or temporal) appearance. (see also pp. )
19While attunement specifies a system's abstract type of awareness or knowledge of constraints which hold and apply in a situation discriminating it from others, the notion of adaptation will characterize the state of structural restrictions which determine a system's behavior most adequate to its environmental conditions.
20This is one of the reasons why an ecological perspective (cite Bateson72) on information processing and cognition (cite Gibson79) is followed here and in (cite Rieg96a, Rieg01).
21 Though the ontological existence of the various constituents of an infon depend on their being picked out by the individuation scheme, the information about the world encapsulated by an infon has the status of being information quite independently of an agent or any scheme of individuation. That is to say, an infon is a fact (i.e. informational) simply by virtue of the way the world is.'' (cite[p. 84] Devlin90)
22The term is meant to relate to Heidegger's philosophy of existence (cite[pp. 49] Heidegger27) where the conditions for grounding and the possibilities for the constitution of experience (fundamental ontology) are analyzed.
23The photograph of a slice of bread is a picture that can be perceived and normally also interpreted, the string of letters 'Brotschnitte' can be perceived as a 12 letter word which is understood only due to proper attunement. Both objects, picture and word have to be recognized and constituted in order to refer to some other object whose particular space-time extension as a real-world slice of bread may render it - even without optical identification or linguistic label - part of a (not necessarily cognitive) factual situation in which - other than the imaging picture and the designating word - it can be eaten to stop hunger.
24In natural language communication this is a common experience for nearly all interlocutors: generally, what we have understood (as its contents) in a conversation, from a text read, etc. is remembered much more easily than the particular object structures of wording, sentences, etc. by which these meanings have been conveyed, exceptions allowed. Other than recognition of acoustic and optic phenomena, memorizing discourse is primarily contents driven and meaning constitutional.
25This allows for the conception of different linear time scales extended to that of differently scaled time cycles, particularly in view of the resolutional power of representations and their semiotic processing in computational models - as addressed below (Eqn. 9, Fig. 5, and Eqn. 14, Fig. 6).
26In view of natural languages discourse there is yet another distinction to be made, although not enlarged upon here, which is due to systems theoretical differences of verbal or auditorially, as opposed to written or optically mediated language environments for interlocuting systems. Whereas the former may be characterized for participating systems as either space-time identical (e.g. face-to-face communication) or spatially relaxed (e.g. videophone conversation), the latter or scripture based interaction will generally dispense with the time coordinates' identity of system-environment pairs concerned, depending on spatial identity of material media (e.g. papyri, mural inscriptions, letters, books, etc.).
27Linguists distinguish cotext or the material embedding of language items within discourse from their context or the situational environment of (items and) discourse as determined by their use in communication.
28The necessity to distinguish sharply between simulation and realization in modeling ecological systems was clarified in desirable detail by Pattee (cite Pattee89) and may be related to the even more fundamental issue addressed by Casti (cite Casti96) who compared the internal structural simplicity (or complexity) of model constructions against their external behavioral complexity (or simplicity) by way of their observable and measurable performances.
29A corpus of pragmatically homogeneous texts consists of discourse which can be considered a random sample from the (virtual) population of (situated) natural language expressions that have (or could have) been produced by interlocutors for communicative purposes in a (specified) situation of verbal interaction.
30However, it should be noted that the contents conveyed cannot always be represented in a language independent way, i.e. by observable operations presented without being understood prior to their (re)presentation. This is why traditional cognitive approaches readily accept a linguistic analysis of propositional language structure as an explication of understanding, and why linguistic semantics in turn appeals to formal logics as an available format for representing NL expressions' propositional functioning. Furthermore, this might be the reason also why the truth functional analysis of propositions can be said to provide an adequate notation for what can be understood as the referential meaning or content of a declarative NL sentence expressing that proposition. And this is, finally, why - for the experimental testing of the modeled SCIP system - we have taken recourse to simple well defined real world situations which can referentially be described by collections of texts of NL sentences that are semantically true. Assembled in a PHT corpus, these texts form the basis for the meaning constituting algorithms implemented to realize the SCIP system's understanding of the texts (the result of) which can be visualized and compared to the (experimental) real world situation, not [!] to a representation of it. (For an implementation, see http://www.ldv.uni-trier.de:8080/rieger/SCIP.html shortly).
31 Constraints give rise to meaning; attunement to constraints make life possible. Some constraints are unconditional or ubiquitous, holding at every location [...]. Others are conditional, holding only under certain special circumstances or conditions. Attunement to conditional constraints is as important to an organism's interaction with the environment as is attunement to ubiquitous constraints.'' (cite[p.94, my italics] BarwisePerry83)
32The FL approach to natural language analysis has recently been characterized (cite Rieg95a, Rieg97a) as an extension to computational linguistics (CL) based on the empirical investigation of performative language data in large text corpora. Its findings are represented and processed employing FST and techniques of fuzzy modeling to achieve higher adequacy of linguistic models than those inspired by competence theoretic approaches.
33 It is important to realize that controls must operate between different descriptive levels, just as constraints must be defined by different descriptive levels. This is necessarily the case for all measurement, recording, classification, decision-making, and informational processes in which a number of alternatives on one level of description is reduced by some evaluative procedure at a higher level of description.'' (cite[p. 251] Pattee72)
34For the discussion of important differences see (cite[p.167] Rieg01)
35 By semiosis I mean [...] an action, or influence, which is, or involves, a coöperation of three subjects, such as sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs.'' (cite[p.282] Peirce06)
36 The concept of natural law in physics is quite distinct from the concept of a constraint. A natural law is inexorable and incorporeal, whereas a constraint can be accidental or arbitrary and must have some distinct physical embodiment in the form of structure. [...] The reason that constraints [of motion] are not redundant or inconsistent with respect to the laws of motion is that they are alternative descriptions of the system. Constraints originate because of a different definition or classification of the system boundaries or system variables even though the equations of constraints may be in the same mathematical form as equations of motion. '' (cite[p. 250] Pattee72)
37 Chomsky's dual conception of language ( i.) as a multitude of (ontogenetically) conceivable internalized languages (IL) instantiating universal grammar abstracted directly as a component [from the mental states and their physical representations of particular minds/brains] of the state attained'' (cite[p.26] Chomsky86), and ( ii.) as the collection of externalized languages (EL), borrowing the term not to refer to any other notion of language ... never characterized in any coherent way'' ( Chomsky, personal communication), but understood - and diverging from Chomsky - to cover all (phylogenetically) possible phenomena of observable language performance, is an admittedly highly attractive one. However, it should not prompt us without examination to subscribe to unwarranted claims of the former's (IL) mental reality and the latter's (EL) abstract objects of some kind''. Instead, IL may well be understood as (systems of) principled features of models rather than properties of the original phenomenon of semiotic cognitive processing which is enacted in and constituted by observable communicative language performance.
38For more detail see (cite[pp.162] Rieg01), where this replacement is introduced as a condition for a system's own (intraneous) experience being complemented by (extraneous) experiences made and communicated by other systems, hereby extending the semiotic systems' acquisition of knowledge and learning potential beyond identical space-time value pairs for processing system-environment (SE) relations.
39In SST situations are conceived both, as real and abstract entities to enable coverage of (pragmatic) issues of context, background, relatedness, etc. of language expressions and their informational import and semantic contents. A real situation is a part of reality, individuated as a single entity according to some scheme of individuation. An abstract situation is a set-theoretical construct, a set of infons, built up out of entities called relations, individuals, locations, and polarities.'' (cite[p.35] Devlin91)
40In Situation Semantics (cite BarwisePerry83), awareness of, or attunement to a constraint is what enables a cognitive agent in a situation to infer that this situation is part of (or tied to) another situation. Attunement does not require language [to be effective, but rather] amounts to a form of familiarity with, or behavioral adaptation to, the way the world operates.'' (cite[p.91] Devlin91)
41It concerns informational content of a cognitive system's beliefs, desires, etc. linking it to actual entities in the world in the appropriate manner.'' (cite[p. 177] Devlin91)
42It even appears that the mediate-immediate distinction can serve to sharply differentiate between (sign based) learning and (signal based) adaptation of systems to their environment. Both require memory whose structures, however, are addressed differently: by signals for immediate evocation of state changes (adaptation), and by signs for mediated and/or virtual state changes (learning).
43In his theory of fuzzy information granulation (TFIG) Zadeh introduces granulation being basic to human cognition as a mode of typified generalization and representation. As an abstract type of (recursive, hierarchical, fuzzy) decomposition it serves to partition an object into a collection of granules, with a granule being a clump of objects (entities) drawn together by a relation that may be instantiated as indistinguishability, similarity, proximity, functionality, etc. In this sense, the granules of the human body are the head, neck, arms, chest, etc. In turn, the granules of a head are the forehead, cheeks, nose, ears, eyes, hair, etc. In general, granulation is hierarchical [and fuzzy] in nature.'' (cite[pp. 112] Zadeh97)
45In view of the wide spectrum that the realm of conceptual structures, mental images, and their organization presents, it is not at all convincing to assume that the organization and functioning of human minds and brains should depend on (or even be identical to) only those very categories and functions which logicians and linguists have been able to isolate from natural languages structures so far. [see pp. pageref above]
46Analogous to Pattee's notion of self-interpretation, self-constraint, and self-rule which are at the basis of life where the separation of genotype and phenotype through language structures took place in the most elementary form.[...] Instead of requiring simply a finite, self-defining system in the abstract symbolic sense, it is more fundamental to require a finite, self-constructing system in the physical sense. This implies a set of constraints which in some coordinated way can reconstruct themselves, as well as establish rules by which other structures can be generated. This coordinated set of constraints would amount to a language structure, that creates a new hierarchical level of organization by allowing alternative descriptions of the underlying detailed behavior.'' (cite[pp. 253] Pattee72)
48Whether these would (have to) qualify as semiotic morphisms which Goguen (cite Goguen96/00) defined as level, constructor, priority, property, and structure preserving mappings S1® S2 of one sign systems S1 to another sign systems S2 is to be investigated.
49Syntagmatic and paradigmatic constraints are considered universal because apparently there is no natural language in the world known not to realize them.
50see also footnotes 2.1 and 3.1
51Assuming a synchronized endo/exo-time and a stable (steady-state) environment, mobility may be specified simply by the pace step per grid number ratio.
52As Fig. 8 suggests, system and environment need not be as far apart but may even be indistinguishable from each other, conflating in the source point (circle) with no spatial extension or timely duration. Such an identity would reduce the categorial framework of spatiality and temporality as well as space-time dynamics to the traditional, non-situational form of characterizing real world phenomena as externally determined and independent from an observer in a naive positivist stance.
53Although on first sight these points appear to be symbolic meaning representations, it is worth mentioning here again that in fact each such point is determined by a fuzzy set or value distribution of pairs of word types associated with numerical values computed from quantitative text analyses.
54see also pp. pageref and footnote 5.1 above.
55Representational formats will be called basal if they can provide a frame for the formal unification of categorial-type, concept-hierarchical, truth-functional, propositional, phrasal, or whatever other intermediate representations.
56It appears that what Pattee (cite Pattee95) named semantic closure and characterized as a specific relation between both the material (performative) and the symbolic (representational) aspects of any organism's behavior is another perspectival view on this phenomenon.
57As will become clear in what follows, this identification concerns the places so far and does not (yet) apply to the objects .
58The concept of knowledge underlying the employment of the adjectival terms here is meant to be understood in the sense that known'' generally refers to having some well established (however controversial experiential, scientific, theoretical, inter-subjective) models to deal with, whereas unknown'' refers to the lack of such models.
59A SCIP system-environment setting - which
will shortly be accessible also via internet (cite RiegFJ02) -
was developed to allow for the experimental testing of varying
results of language understanding against changing
processes of SPOL relations described. The test design
hinges on the idea that SCIP will have to operate on and produce
the structures which are a condition for and a results of such
processing.