A man, viewed as a behaving system, is quite simple. The apparent complexity of his behavior over time is largely a reflection of the complexity of the environment in which he finds himself ... provided that we include in what we call man's environment the cocoon of information, stored in books and long-term memory, that man spins about himself. 1
As long as the concept of meaning was conceived as some independent and pre-existing entity, very much like that of physical objects in the real world, meaning appeared to be analysable and representable accordingly, i.e. as sets of features and as entries in a knowledge base whose elements and their mutual relations stand for certain other entities which are taken to be represented by these data base entries due to the labels or signs attached whose functions or meanings are known and understood. Thus, semantic net models depict meanings as a system of relations between signs and designata whose representations as labeled nodes and arcs make up structured sets of elements whose meanings are signalled by language symbols attached to them. Within this frame of semantics as a theory about the nature of reality (Lakoff 1988) the problem of semantic grounding cannot be addressed, the related questions of how a symbolic expression may serve as a label and on what grounds it gets associated with a node in order to let this node be understood to stand for the entitity (meaning or object) it is meant to represent, cannot even be posed. However, these questions have to be realized, explored, and eventually answered:
it has to be realized that there are certain entities which-beyond their physical existence in the world-are (or become) signs and have (or acquire) interpretable meanings that can be understood in the sense of knowing what the signs signify and stand for (whereas other entities in the world do not). it has to be explored how such (semiotic) entities may be constituted and how the meaning relation be established on the basis of which observable regularities (uniformities), controlled by what constraints (syntagmatic and paradigmatic), and under which boundary conditions of situational configurations for communicative interactions (pragmatics). it has to be answered why some entities may signify others by serving as labels or representations for them (or rather by the labeling and representational functions these entities serve), instead of being just named according to their positions, load values and/or patterns exhibited in a representational system of semiotic/non-semiotic entities.
In doing so, a semiotic paradigm based upon some ecological concepts of the theory of information processing systems will be followed which hopefully may allow to avoid (if not to solve) a number of spin-off problems, which originate in the traditional distinction and/or the methodological separation of the meaning of a language's term (or rather, its format of representation) from the way it is employed in discourse. It appears that failing to mediate between these two sides of natural language semantics, phenomena like creativity, dynamism, efficiency, vagueness, and variability of meaning-to name only the most salient-have fallen in between, have stayed (or be kept) out of the foci of interest, or have been overlooked altogether (Rieger 1991a, 1991b). Moreover, classical formal theoretic approaches to natural language semantics which are based upon constraints of propositional constructions and confined to the sentence boundary are badly in want of operational tools that may allow to bridge the gap between formal theory of language description (competence) and empirical analysis of language usage (performance) felt to be responsible for the unwarranted abstractions from fundamental properties of natural languages.
In terms of the theory of information systems, texts-whether
internal or external to the systems-function like virtual
environments3.
Considering the system-environment relation, virtuality
may 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 this dispensation of identity-for short:
space-time-dispensation-is not only conditional for the possible distinction
of (mutually and relatively independent) systems from their
environments, but establishes also the notion of
representation.
Accordingly, immediate or space-time-identical system-environments
existing in their space-time-identity may well be distinguished from mediate or space-time-dispensed
system-environments whose particular representational form (texts)
corresponds to their particular status both, as language material (being signs),
and as language structure (having meaning).
This double identity
calls for a particular modus of actualisation (understanding)
that may be characterized as follows:
For systems appropriately adapted and tuned to such environments
actualisation consists essentially in a twofold embedding to realize
the space-time-identity of pairs of immediate system-environment coordinates which will let the system experience the material properties of texts as signs (i.e. by functions of physical access and mutually homomorphic appearance). These properties apply to the percepts of language structures presented to a system in a particular discourse situation, and the representational identity of pairs of mediate system-environment parameters which will let the system experience the semantic properties of texts as meanings (i.e. by functions of emergence, identification, organisation, representation of structures). These apply to the comprehension of language structures recognized by a system to form the described situation
Hence, according to the theory of information systems, functions like interpreting signs and understanding meanings translate to processes which extend the fragments of reality accesssible to a living (natural and possibly artificial) information processing system. This extension applies to both, the immediate and mediate relations a system may establish according to its own evolved adaptedness or dispositions (i.e. innate and acquired structuredness, processing capabilities, represented knowledge).
The actualisation of environments, however, does not merely add to the amount of experiencial results, but constitutes instead a significant change in experiencial modus. This change is characterized by the fact that only now the processes of experience may be realized as being different and hence be separated from the results of experience which may thus even be represented, other than in immediate system-environments where result and process of experience appear to be indistinguishable. Splitting up experience in experiencial processes and experiencial results-the latter being representational and in need for actualisation by the former-is tantamount to the emergence of virtual experiences which have not to be made but can instead just be tried, very much like hypotheses in an experimental setting of a testbed. These results-like in immediate system-environments-may become part of a system's adaptive knowledge but may also-different from immediate system-environments-be neglected or tested, accepted or dismissed, repeatedly actualized and re-used without any risk for the system's own survival, stability or adaptedness.
The experimental quality of textual representations which increases the potentials of adaptive information processing immensely, will have to be constrained simultaneously by dynamic structures, corresponding to knowledge. The built-up, employment, and modification of these structural constraints4 is controlled by procedures whose processes determine cognition and whose results constitute adaptation. Systems properly adapted to textual system-environments have acquired these structural constraints (language learning) and can perform certain operations efficiently on them (language understanding). These are prerequisites to recognizing mediate (textual) environments and to identify their need for and the systems' own ability to actualize the mutual (and trifold) relatedness constituting what Peirce called semiosis 5. Systems capable of and tuned to such knowledge-based processes of actualisation will in the sequel be referred to as semiotic cognitive information processing systems (SCIPS).
Following an attempt to classify approaches in cognitive science, we may discern four6 categories of approaches in modelling cognition:
Whereas both these approaches apparently draw on the traditional rationalistic paradigm of mind-matter-duality-static the former, dynamic the latter-in presupposing the external world structure and an internal representation of it, the third and fourth category do not:the cognitive approach presupposes the existence of the external world, structured by given objects and properties and the existence of internal representations of (fragments of) this world, so that cognitive systems' (observable) behaviour of action and reaction may be modelled by processes operating on these structures; the associative approach is described as a dynamic structuring based on the model concept of self-organization with the cognitive system constantly adapting to changing environmental conditions by modifying its internal representation of them.
the enactive approach may be characterized as being based upon the notion of structural coupling. It disposes of the assumption-whatever else the semantics of coupling might suggest-of an external world and a system's internal representation of it, but considers instead some unity of structural relatedness to be fundamental of-and the (only) condition for-any abstracted or acquired duality that philosophical realism has in the past (or might in future) come up with; the semiotic approaches focus on the notion of semiosis and may be characterized by the process of enactment too, supplemented, however, by the representational impact. It is considered fundamental to the distinction of e.g. cognitive processes from their structural results which-due to the traces these processes leave behind-will emerge in some form of knowledge whose different representational modi comply with the distinction of internal or tacid knowledge (i.e. memory) on the one hand and of external or declarative knowledge (i.e. texts) on the other 7.
According to these categories of cognitive modelling, computational semiotics can be characterized to be aiming at the dynamics of modelling natural language meaning within the frame of ecological information processing.
Taking human beings as the most efficient semiotic cognitive information processing systems (SCIPS) whose outstanding sign and symbol manipulation and understanding capabilities are but a consequence of the very efficient knowledge organisation, representation, and modification processes they apply, then the observable structures resulting from these processes, namely natural language discourse provides a cognitively interesting meaning representation system whose outstanding structuredness in the aggregated form of text corpora from communicative situations may serve as a guideline (Rieger 1977) rarely followed in research yet. In doing so, however, it will be necessary to pass on from traditional approaches in linguistics proper analysing introspectively the propositional contents of singular sentences as conceived by ideal speakers/writers to semiological approaches based upon the empirically well founded observation and rigourous mathematical description of global regularities in masses of texts produced by real speakers/writers in actual situations of either performed or intended communication. Only such new approaches will give a chance to reconstruct procedurally both, the significance of entities and the meanings of signs as a function of a first and second order semiotic embedding relation of situations (or contexts) and of language games (or cotexts) which corresponds to the two-level actualisation of SCIPS s.
Whereas traditional approaches in artificial intelligence research (AI) or computational linguistics (CL) model cognitive tasks or natural language understanding in information processing systems according to the realistic view of semantics, it is argued here that meaning need not be introduced as a presupposition of semantics but may instead be derived as a result of procedural modelling8 as soon as a semiotic line of approaches to cognition will be followed.
It is the semiotic foundation (Rieger 1985e:, 1989) that adds an ecological dimension to cognitive models (Rickheit/Strohner 1993) of natural language processing extending them explicitely to comply with those conditions which sign quality object domains produce, whether in processes of natural language performance (intention, production, reception, and understanding of discourse) or in the (explanatory, derivational, or procedural) modelling of these processes. Thus, for semiotic models the ecological paradigm (Bateson 1979, Maturana 1978, Maturana/Varela 1980) essentially translates to an obligation according to which the entities any system model starts with are to be kept (conceptually) as simple and (in number) as small as possible in order to avoid presupposing complex entities (structures or processes of some kind) where these could also be derived or their emergence be simulated by the model. This obligation applies very much to natural language meaning and in the case of SCIPS s boils down to the necessity to include the situational context of language performance from the very start of the modelling process instead of extending or modifying some model result by adding a set of contextual parameters to it. Therefore, the present approach is based upon a phenomenological (re-)interpretation of the formal concept of situation and the analytical notion of language game. The combination of both lends itself easily to operational extensions in empirical analysis and procedural simulation of associative meaning constitution which will grasp essential parts of semiosis.
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. 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 renders them interpretable.
In semiotic sign systems like natural languages, such uniformities also appear to be signalled more basically by word-types whose employment as word-tokens in texts exhibit a special form of structurally conditioned constraints. Not only allows their use the speakers/hearers 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 referencial) aspects of event-types and how these are related by virtue of word uniformities accross phrases, sentences, and texts uttered. Thus, as a means for the intensional (as opposed to the extensional) description of (abstract, real, and actual) situations, the regularities of word-usages may serve as an access to and a representational format for those elastic constraints which underly 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.
Owing to Barwise/Perry's new approach-and notwithstanding its traditional (mis)conception as duality (i.e. the independent sign-meaning-view) of an information processing system on the one hand which is confronted on the other hand with a prefixed external reality whose accessible fragments are to be recognized as its environment-this notion of situation proves to be pivotal for an empirical extension to their theory of semantics. Not only can it be employed to devise a procedural model for the situational embeddedness of cognitive systems as their primary means of mutual accessability (Rieger/Thiopoulos 1989, Rieger 1991b), but also does it allow to capture the semiotic unity as specified by the idea of language games.
Trying to model language game performance along traditional lines of cybernetics by way of, say, an information processing subject, a set of objects surrounding it to provide the informatory environment's input, and some positive and/or negative feedback relations10 between them, would hardly be sufficient to capture the cognitive dynamism that enactive systems of knowledge acquisition and meaning understanding are capable of due to their elastic constraints, i.e. the restrictions which hold for the agglomerative or syntagmatic and the selective or paradigmatic structuring of language units in discourse.
The philosophical concept of language games as specified by the formal notion of situations, not only allows for the formal identification of both, the (internal) structure of the cognitive subject with the (external) structure of its environment. Being tied to the observables of actual language performance, communicative language usage opens up an empirical approach to procedural semantics. Whatever can formally be analysed as uniformities in Barwiseian discourse situations may eventually be specified by word-type regularities as determined by co-occurring word-tokens in pragmatically homogeneous samples of language games. Going back to the fundamentals of structuralistic descriptions of regularities of syntagmatic linearity and paradigmatic selectivity of language items, the correlational analyses of discourse will allow for a multi-level word meaning and world knowledge representation whose dynamism is a direct function of elastic constraints established and/or modified in communicative interaction by use of language items.
As has been outlined in some detail elsewhere (Rieger 1989, 1990; Rieger/Thiopoulos 1993), the meaning function's range may be computed and simulated as a result of exactly those (semiotic) procedures by way of which (representational) structures emerge and their (interpreting) actualisation is produced from observing and analyzing the domain's regular constraints as imposed on the linear ordering (syntagmatics) and the selective combination (paradigmatics) of natural language items in communicative language performance. For natural language semantics this is tantamount to (re)present a term's meaning potential by a fuzzy distributional pattern of the modelled system's state changes rather than a single symbol whose structural relations are to represent the system's interpretation of its environment. Whereas the latter has to exclude, the former will automatically include the (linguistically) structured, pragmatic components which the system will both, embody and employ as its (linguistic) import to identify and to interpret its environmental structures by means of its own structuredness.
Implemented, such a system eventually may well lead to something like machine-simulated cognition, letting information be processed as a means of constituting a (system-dependent) view of reality from the system's (linguistically structured) environment. It is argued here that its faculty of representing reality may be reconstructed as a complex function of those regularities which elements of communicative sign usage exhibit on different levels of linguistic description from morphs to words and discourse.
Under the notion of lexical relevance and semantic disposition (Rieger 1985b, 1985d) a corresponding meaning representation has been defined and tested whose parameters may automatically be detected from natural language texts and whose non-symbolic and distributional format of a vector space notation allows for a wide range of useful interpretations.
The basically descriptive statistics used to grasp these relations on the level of words in discourse are centred around a correlational measure (Eqn. 5) to specify intensities of co-occurring lexical items in texts, and a measure of similarity (or rather, dissimilarity) (Eqn. 8) to specify differing distributions of correlation values. Simultaneously, these measures may be interpreted semiotically as providing for set theoretical constraints or formal mappings (Eqns. 6 and 9) which model the meanings of words as a function of differences of usage regularities.
As a first mapping function a allows to compute the relational
interdependence of any two lexical items from their textual
frequencies. For any text corpus
| (1) |
| (2) |
| (3) |
| (4) |
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)\tilde] : V ×V ® I
can be conditioned on xn Î V which yields a crisp mapping
| (6) |
| (7) |
Thus, d may serve as a second mapping function
to represent any item's differences of usage regularities measured against
those of all other items. As a fuzzy binary relation, also
[(d)\tilde] : C ×C ® I
can be conditioned on yn Î C which again yields a crisp mapping
| (9) |
| (10) |
By identifying zn Î S with the numerically specified elements of
potential paradigms, the set of possible combinations S ×S
may structurally be constrained and evaluated without (direct
or indirect) recourse to any pre-existent external world.
Introducing a Euclidian metric
| (11) |
As a result of the two-stage consecutive mappings any meaning point's position in SHS is determined by all the differences (d- or distance-values) of all regularities of usage (a- or correlation-values) each lexical item shows against all others in the discourse analysed. Without recurring to any investigator's or his test-persons' word or world knowledge (semantic competence), but solely on the basis of usage regularities of lexical items in discourse resulting from actual or intended acts of communication (communicative performance), text understanding is modelled procedurally by processes to construct and identify the topological positions of any meaning point zi Î áS,zñ corresponding to the vocabulary items xi Î V which can formally be stated as composition of the two restricted relations (d)\tilde | y and (a)\tilde | x (Fig. 1).
Processing natural language texts the way these algorithms do would appear to grasp some interesting portions of the ability to recognize and represent and to employ and modify the structural information available to and accessible under such performance. A semiotic cognitive information processing system (SCIPS) endowed with this ability and able to perform likewise would consequently be said to have constituted some text understanding. The problem is, however, whether (and if so, how) the contents of what such a system is said to have understood can be tested, i.e. made accessible other than by the language texts in question and/or without committing to a presupposed semantics determining possible interpretations.
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 of a multi-level conceptual knowledge representation system (Rieger 1989). Essentially, it separates the format of a basic (stereotype) word meaning or concept representation from its latent relational forms of organization for particular cognitive purposes. Whereas the former may be thought of as a rather stable (or long-term), topologically structured (associative) memory, the latter can be characterized as a collection of structuring procedures which re-organize the memory data according to cognitive tasks to be solved under situational (or short-term) conditions11.
As we have separated cognitive processes from their resultant structures above12, so we may distinguish here between the long-term structure as an addressable representation of knowledge (stereotype or concept) and its short-term process in a situational embedding (employment or activation) with the semiotic 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 above13 may be mediated by processes operating on some common, basal representational structures14 whose efficient reorganisation can be modelled procedurally to result in a-more or less subjective-internal (or endo-)view the system develops, a n d in a-more or less objective-external (or exo-)view of the surrounding environment that constitutes reality.
To find out (and preferably be able to test) what of the structural information inherent in natural language discourse-defined a n d structured by the text analytical processes described above15-might be involved in mediating or constituting that duality, an experimental setting has been designed. It is based on the assumption that some deeper representational level or core structure-similar to the one modelled by SHS-might be identified which could be considered a common base for different notions of meaning developped by theories of referential and situational semantics as well as some structural or stereotype semantics.
To give a general view of the approach first, the experimental setting is pictured by a mobile system in a two dimensional environment with some objects at certain places to identify. The system's channels of perception 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 an artificially abstracted 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 by the system, but will instead be constituted according to the system's (co- and contextually restricted) susceptibility and processing capabilities to (re-)organize the environmental data a n d to (re-)present the results in some dynamic structure which determines the system's knowledge (susceptibility), learning (change) and understanding (representation).
This postulate, obviously, rules out immediately any traditional form of cognitive modellings which do not see the need of such a differentiation. They are satisfied instead with well established formalisms (in syntax, semantics, predicate logics) not only to distinguish, describe, and represent different levels of natural language structures but consider them also appropriate to determine and control the processing of what these levels are meant to model. Consequently, corresponding knowledge bases representations are conceived which cognitive processes are believed to operate on when employed to analyse and interpret natural language expressions. Thus, cognitive modelling of language understanding has narrowed the general (and semiotic) scope of knowledge acquisition and knowledge based processing of signs events-via re-usable results in some representational format (memory)-to the formatting of (both world and linguistic) knowledge and the application of rules of syntax and semantics. Ascribing syntactic structures to sentences whose truth-functional interpretation is determined by a referential semantics which in turn seems to allow for the definition of predicate meanings according to properties believed to be observed, recognized, indentified, and named in the world around and external to the cognitive systems, is to favour a very particularized understanding of language understanding which is hardly tenable.
As it appears by no means convincing why some (well understood) formalisms representing certain functional results on different levels of (more or less arbitrary) abstraction should also provide the only levels or moduls to study and investigate the (yet enigmatic) processes related to (or even underlying) these (or other cognitive) functions in language processing, this hypothesis common to models of language understanding in cognitive linguistics is questioned.
To enable an intersubjective scrutiny, it is suggested here that the (unknown) results of an abstract system's (well known) acquisition process is compared against the (well known) traditional interpretations of the (unknown) processes of natural language meaning constitution16. To achieve this, it has to be guaranteed that
a corpus of pragmatically homogeneous texts providing the system's environmental data is compiled as a collection of (natural language) expressions of true propositions denoting the system-object-relations according to some specified syntax and semantics (representing the exo- view or described situations), and the system's internal picture of its surroundigs (representing the endo- view or discourse situations) which will (and can) be derived from this textual language environment other than by way of propositional reconstruction, i.e. without syntactic parsing and semantic interpretation of sentence structures.
Therefore, the exo- knowledge allowing the designers of the experimental setting to control the propositional encoding and decoding of environmental information in texts which the system in a specified environment would process, had to be kept strictly apart from and was essentially not to be included in the SCIP system's endo- capacities. Thus, the system's own non-propositional processing would allow to come up with some results which cannot be interpreted as mere repetitious reproductions of knowledge structures which the system had been endowed with externally, but which instead may be considered the system's internal representation quite comparable (however different in format) to the exo- view of the environment.
moving (linearly) about that plane in a (limited) number of directions and at a certain pace. Then, for any point that the system may occupy in that referential plane there is (at least) one true proposition denoting the relation between the system's position and the object's location. Natural language expressions of such true propositions denoting factual position-location- relations (which will vary with the system moving) can easily be generated given a limited vocabulary, a simple syntax and semantics.
The three main components of the experimental setting, the system, the environment, and the discourse are specified by sets of conditioning properties. These define the SCIP system by way of a set of procedural entities like orientation, mobility, perception, processing (Tab. 2), the SCIP-environment is defined as a set of formal entities like plane, objects, grid, direction, location (Tab. 3), and the SCIP-discourse material mediating between system and environment is structured first by a number of part-whole related entities like word, sentence, text, corpus (Tab. 4) of which sentence and text require further formal restrictions to be specified by a formal syntax (Tab. 5) and a referential semantics (Tab. 6).
The strict separation between the process and its result on the system's side now corresponds to the sharp distinction between the formal specification to control the generation of referentially descriptive language material and its processing within the experimental SCIP setting. Whereas the given definitions of word and corpus suffice to specify the elementary and global dimensions of the language material for its non-propositional processing, the intermediate dimensions of sentence and text want further specification.
A (very simple) phrase-structure grammar (Tab. 5) and a reference semantic (Tab. 6) with different (crisp or possibly fuzzy) interpretations serve the purpose. Together, they determine the generation of situational adequate texts that consist of true and correct sentences describing the location of an object relative to the position the system might take. Localities are denoted by simple local predicate expressions composed of cores like ''on the left'' or ''on the right'' and ''in front'' or ''behind'' together with hedges like ''extremely'' or ''very'' or ''rather'' and ''nearby'' or ''faraway'' to form sentences like e.g. ''A triangle lies rather nearby on the left.'' - ''A square lies very faraway in front.'' - etc.
This leads to the schematic diagram (Fig. 3) of the general set up, the SCIP system, and its environment. It illustrates the situational components conditional for the external view of the environment or exo- reality-as specified (by Tab. 3)-mediated by referentially true and situational adequate textual descriptions (language training material) generated according to the syntax and semantics (Tab. 5 and Tab. 6) for the SCIP system-as specified (by Tab. 2)18-whose (language) perception, (cognitive) processing, and (internal) structuring will result in the dynamic built-up of its own or endo- view of the environment. How can it be tested and evaluated to correspond-at least partially-with the exo- view which also happens to be ours but may certainly not necessarily be identified with it?
In the course of the processing, the two-level consecutive mappings ( Tab. 1 and Fig. 1)22 result in the semantic hyper space (SHS) structure (as declared by Eqns. 10 and 11)23 whose vector space intrinsic data structure can be made visible in a three stage process:
In a second step, pairs of hedged predicate clusters as produced by the dendrogram cuts may referentially be decoded and numerically be specified for an intermediate representational frame or working structure Endo1. With this end, the same (crisp) interpretations of hedged core predicate labels are used (Tab. 7) which also served to encode the denotational meaning in the propositional texts of the language training material. However, whereas the encoding was derived from the exo- viewed (or factual) object locations (n,m) relative to changing system positions (x,y) at any point in the referential plane (Fig. 2) yielding numerical distances | m-x | , | n-y | for some choice of referential grid, ÂR(m,n); m=x= 10, n=y= 10 according to the defined semantics of hedged core predicates, the decoding is now derived from the system's own or endo- expectations visualized as a plane or matrix Endo1i,j; i= 20, j= 20 with the system fixed in central position relative to its directionally determined orientations of potential object-locations (Tab. 8).
It is this relation that now translates the structural adjacencies of meaning points identified by pairs of hedged core predicate labels. Their numerical hedge interpretation yields the distance values and their directional core interpretation determines the regions of object locations. The representational frame selected for these endo- viewed regions is to be found in overlapping referential locations allowing to denote everything that is ''on the left'', ''in front'', ''on the right'' of the system or ''behind'' it. These directional overlaps combine to form a coordinate system of four quadrants each with the referential grid's cardinality, and the SCIP system in the center.
To illustrate this translation, the matrix Endo1i,j; i= 20, j= 20 (Tab. 8) contains the number of marks per grid point which are identified according to the corresponding distance values of clustered hedge predicate pairs, and which are distributed around the system's central position (i= 10, j= 10) for the southern orientation (O-value of Tab. 2). The profile of Endo1i,j (Fig. 5) allows quite clearly to see that it is but a 3-dim- translation of the 2-dim- structure of the cluster dendrogram (Fig. 4) with the base being formed by the core predicate adjacencies to denote potential referential areas from a centrally positioned system's view.
The Endo1i,j data (Tab. 8) serves as base
for the following third step of a line- and column-wise transform which
results in a new mapping Endo2m,n (Tab. 9)
according to the summation equation
| (12) |
The matrix Endo2m,n (Tab. 9) contains the data for the external observer's representation of the endo- view that the system has computed from the training corpus of texts describing object locations relative to system positions in the reference plane (Fig. 2). This becomes evident when looking for highest m,n-values in the matrix which reveals 295 at (3, 8) and 291 at (6, 3) to be exactly or very near the object locations which were encoded in the training corpus of texts as generated to form the system's language environment. A (two-dimensional) 2-dim- scattergram of Endo2 (Fig. 6) gives an overall picture as a pattern of polygons which connect points of even referential likelihood or so-called isoreferentials denoting potential object locations quite clearly, however fuzzy. The 3-dim- scattergram of the same data (Fig. 7) pictures the differences in reference potentials in a more obvious way.
It is to be noted here, too, that the initial 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 abstracting from their situational embedding. As soon as gradation (or fuzziness) is included as a consequence of such co- and contextual situatedness-i.e. by way of textual language descriptions of object locations relative to system positions (described situations) and their actualization or understanding by the system concerned (discourse situations)-the representational frame is immediately extended by structural or pragmatic information25 (Weizsäcker 1974) which may conventionally be represented only by adding another dimension. What may be observed on the representational level as a transition from the initial reference plane (Fig. 2) to the 2-dim- image of the system's endo- view of it (Fig. 6), whose inherent structural information gives rise to represent the isoreferentials in another (third) dimension (Fig. 5), may find an analogue correspondence on the procedural level of the processes which have been dealt with in view of their semiotic potential so far.
As may be gathered from what has been outlined so far, the non-propositional processing of a set (corpus) of sets (texts) of correct and true language expressions (sentences) of propositions describing (fixed) object locations relative to (changing) system positions resulted in an internal memory of labelled meaning points in a vector space (SHS) format whose intrinsic structure was made visible by three consecutive stages of representations. These visualizations were based on crisp interpretations (Tab. 7) of the hedges. Using fuzzy definitions instead (Tab. 8) to interpret the adjacencies of hedged core predicate labels from the cluster analysis (Fig. 4)26 will-as is to be expected-produce comparable images of emerging structuredness which can be visualized again in the form of isoreferentials (Fig. 6). What is surprising though in doing so is the fact that these new exo-representations of the system's endo- view appear to be a more immediate image of the referential space structure under fuzzy 1.1 interpretations of hedges, as they are derived without an intermediate transform like Endo1-Endo2 above (Eqn. 12).
A still very tentative explanation may be offered by assuming that the fuzzy interpretation of hedged core predicate adjacencies on this (representational) level appears to have a similar effect as changing positions of the system would produce on the situational level to generate more language material. Described by varying but definite relations of (object) locations and (system) positions under crisp interpretation of hedges, such variations seem to become expressed also by the fuzzy 1.1 definitions of hedge predicates.
This might be the reason-pending thorough testing under varying object locations-for an overall structure being found to emerge from non-propositional processing of these situational descriptions that does not need transformation in order to reveal most likely object locations, but anticipates them by an interpretational substitute of material description, i.e. the fuzzy denotational definitions.
It was hypothesized that the notion of reference and denotation as specified by realistic semantic theories favoured in competence linguistics might be reconstructed also within structural semantics based on theories of linguistic performance and an ecological understanding of informational systems. Drawing on the procedural modelling and numerical instantiation of processes that simulate the constitution of meanings and their distributional or fuzzy representations in vector-space formats, an abstract semiotic cognitive information processing system (SCIPS) was introduced that operates in a well defined, experimental language environment as a meaning acquisition and understanding device.
For the purpose of evaluating the understanding of meanings which the system might acquire in the course of its language processing, particular pains were taken to allow the system's endo- view of its environment to differ observably from the exo- view of that same environment. In order to show that a semiotic, essentially non-propositional processing of language expressions can detect very much the same referencials which a propositional and truth-functional processing of these expressions would decode, the exo- view of the environment was formalized by constraints explicidly stated. These constraints-as given by the syntax and semantics specifying correct and true descriptions of object locations relative to system positions-do not, therefore, presuppose the existence of an objective reality external to the system or the system-environment designers (observers), but introduce a formal model to specify the conditions under which the results of propositional vs. non-propositional processing can be compared and evaluated either to the negative or to the positive.
The author is quite certain to have produced some evidence for the latter.
*English version of an invited lecture for the 125th Heraeus-Seminar on ``The concept of information: an interdisciplinary perspective'' of the Wilhelm and Else Heraeus Foundation, Technical University of Cottbus, Germany, March 1st- 4th, 1994, published in: Kornwachs, K./ Jacoby, K. (Eds.): Information. New Questions to a Multidisciplinary Concept. Berlin (Akademie) 1996, pp. 285-315.
**The author is indebted to discussion of central ideas of this paper with Petra Badry, Kathrin Gieseking, Beate Oerder, Maria Reichert and Ralph Wagner whose substantial contributions (of varying intensity and uneven distribution during different phases of the project) in converting procedural models to operational programs are highly appreciated. The errors are his own as always.
1Simon (1982), p. 127
2According to standard theory there is no direct genetic coding of experiencial results but rather indirect transmission of them by selectional advantages which organisms with certain genetic mutations gain over others without them to survive under changing environmental conditions.
3Simon's (1982) remark ''There is a certain arbitrariness in drawing the boundary between inner and outer environments of artificial systems. ... Long-term memory operates like a second environment, parallel to the environment sensed through eyes and ears'' (pp. 104) is not a case in point here. Primarily concerned with where to place the boundary, he does not seem to see its placing in need to be justified or derived as a consequence of some possibly representational processes we call semiotic. As will become clear in what follows, Simon's distinction of inner (memory structure) and outer (world structure) environments misses the special quality of language signs whose twofold environmental embedding (textual structure) cuts accross that distinction, resolving both in becoming representational for each other.
4What Simon (1982) calls Memory in accordance with his questioning of the inner-outer-distiction of cognitive systems and their environments.
5By 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. (Peirce 1906, p. 282)
6There were only the first three of these four approaches distinguished by Varela/Thompson/Rosch (1991).
7Whereas tacid knowledge will not be represented other than by the immediate system-environment's corresponding status, explicit knowledge is bound to acquire some formal properties in order to be representable and become part of mediate system-environments. Natural languages obviously provide these formal properties-as identified by research in linguistic competence (knowledge and acquisition of language)-whose enactment-as investigated in studies on natural language performance (production and understanding of texts)-draws cognitively on both bases of (explicit and tacid) knowledge.
8Procedural models denote a class of models whose interpretation is not (yet) tied to the semantics provided by an underlying theory of the objects (or its expressions) but consist in the procedures and their algorithmic implementations whose instantiations as processes (and their results) by way of computer programs provide the only means for their testing and evaluation. The lack of an abstract (theoretical) level of representation for these processes (and their results) apart from the formal notation of the underlying algorithms is one of the reasons why fuzzy set and possibility theory-Zadeh (1965), (1975), (1981)-and their logical derivates were embraced to provide an open and new procedural format for computational approaches to natural language semantics without obligation neither to reject nor to accept traditional formal and modeltheoretic concepts.
9''There are ways of using signs simpler than those in which we use the signs of our highly complicated everyday language. Language games are the forms of language with which a child begins to make use of words. [ ... ] We are not, however, regarding the language games which we describe as incomplete parts of a language, but as languages complete in themselves, as complete systems of human communication.'' (Wittgenstein 1958, pp. 17 and 81; [my italics ])
10''[... ] feedback is a method of controlling a system by reinserting into it the results of its past performance. If these results are merely used as numerical data for the criticism of the system and its regulations, we have the simple feedback of control engineers. If, however, the information which proceeds backward from the performance is able to change the general method and pattern of perfomance, we have a process which may well be called learning.'' (Wiener 1956, p. 60)
11This notion corroborates and extends ideas also expressed within the theories of priming and spreading activation (Lorch 1982) allowing e.g. for the dynamic and task-oriented generation of paths (along which activation might spread) allowing priming to be modelled as cognitive function rather than one of its presupposed conditions.
14Representational 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 representations.
16The concept of knowledge underlying this use here may be understood to refer to known as having well established (scientific, however controversial, but at least inter-subjective) models to deal with, whereas unknown refers to the lack of such models.
20cf. Tab. 5 and Tab. 6, p. pageref
21cf. p. pageref and pp. pageref-pageref
24This impossibility is derived from the formal definitions specified by the semantics (Tab. 6), not by our own knowledge or intuitions.
25For a detailed discussion confer Gernert (1995) and Kornwachs (1995) in this volume.