Situations, Topoi, and Dispositions.
On the phenomenological modelling of meaning¹

Burghard B. Rieger, Constantin Thiopoulos
Deptment of Computational Linguistics, FB II: LDV/CL - University of Trier
Postf. 3825, D-5500 TRIER, West Germany

December 12, 1988

0 Introduction

Submitting to the dualism of the rationalistic tradition of thought and its notions of some (objective) reality and the (subjective) conceptions of it, Barwise/Perry (1983) have presented a new approach to formal semantics which, essentially, can still be considered a mapping of this duality, mediated though by their notion of situation. Within their relational model of meaning, any language expression is tied to reality in two ways: by the discourse situation allowing its meaning being interpreted and by the described situation allowing its interpretation being evaluated truth-functionally. This is achieved by recognizing similarities or invariants between situations that structure a system's surrounding environments (or fragments thereof). Mapping these invariants as uniformities across situations, cognitive systems attuned to them are able to identify and understand those bits of information which appear to be essential to form these systems' particular view of reality: a flow of types of situations related by uniformities like individuals, relations, and time-space-locations which constrain "a world teaming with meaning"² to become interpretable fragments as persistent courses of events.

Thus, the notion of situation allows for the formal identification of both, the (internal) structure of the cognitive subject with the (external) structure of its environment as perceived as a situational fragment of the objective world, a n d the systematic constraints exhibited by related situations with the persistency of courses-of-events for those systems that are properly attuned.

Barwise/Perry apparantly concede that the identification and interpretation of external structures is to be conceived as a form of information processing which (natural/artificial) systems - due to their own cognitive structuredness - are (or ought to be) able to perform. However, these processes or the structures underlying them have not so much resulted from but rather presupposed to the formal analyses and constructions which the authors of situation semantics have developed sofar.

We will argue that meaning need not be introduced as a presupposition but may instead be derived as a result of semiotic modelling, and that it is the concept of situation which lends itself to a phenomenological interpretation. Owing to Barwise/Perrys formal conception of it - being (mis)conceived as a 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 an external reality whose accessible fragments are to be recognized as its environment - the notion of situation can well be employed to devise a formal model that captures the semiotic unity (i.e. the contextual-use-meaning view) of any cognitive systems' situational embeddedness constituting its being-in-the-world ( In-der Welt-sein) as the primary means of accessability. For a theory of natural language semantics this is tantamount to (re)present a term's meaning by including rather than excluding the way it is used in communicative interaction ( Wittgenstein 1958) as specified by discourse situations.

In doing so, we hope to avoid (if not to solve) a number of problems, which originate in the traditional distinction and/or separation of a linguistic term's meaning from the way it is employed in discourse: phenomena like creativity, efficiency, dynamism, vagueness, and variability of meaning - to name only the most salient - fall in between, stay out of the focus of interest, or are being ignored altogether. Moreover, the classical approach in formal theory of semantics is confined to the sentence boundary of propositional constructions and in want of operational tools to bridge the gap between formal theory of language description (competence) and empirical analysis of language usage (performance).

Thus, in a phenomenological stance, the propositional notion of situation can be (re)interpreted (1) and employed to model the identity of (pre-theoretic) structures of the world and its interpretation within a formal approach to semantics as topos (2). Its generality allows for an empirical approach to word meaning, based upon the correlational analyses of discourse to yield á proceduraì notioî oæ meaninç aó ô semantiã disposition (3) Together thes approache allo fo the development of a process-oriented system representing cognitive experience and semiotic structuring procedurally. Implemented, this may eventually lead to something like machine-simulated, dynamic models of perceived reality by a system and its surroundings (Um-Welt), accessible through and structured by world-revealing (linguistic) elements of communicative language use.

1 The propositional approach

A set of propositions is a mathematical model of a partial world. In contrast to possible-world semantics, situation semantics works bottom up, i.e. it begins with a situation, as a propositional model of a minimal world, regarding possible extensions of it as partial worlds. A total world does not need to exist.

For R relations, I individuals and T = { 0, 1} R ×I ×T is the set of situations. T are not truth values, but a positive or negative characteristic of the accessability of the world revealed (Welterschließung). For L spatio-temporal locations, COE is the set of courses of events

The elements of PERS are called persistent coes.

The coes that stand for possible world descriptions are the persistent ones. They model the world view captured relative to the cognitive systems' point-of-view, i.e. subject-dependently. Every such partial world can be seen as a limit of an approximation. A situation described by a speaker represents for the hearer a part of the speaker's world. It can be extended, according to the hearer's own knowledge. Cognitively speaking, this is the situational starting point of the approximation which consists in the hearer's extension of it. The coe achieved captures the hearer's (re-)construction of his own world and becomes an expression of its noetic structure. The limit of the approximation is a maximal world description (not the maximal one), which from a phenomenological point-of-view can be thought of as the structure of correlated noemata.

According to Husserl (1976, p.109), the world as noemata is a stratified sphere of

The actual noemata which are produced from the noeses activated through objects which are in the focus of attention;

The background noemata, which constitute the horizon of the actual ones;

The possible noemata, which reflect the noetic structure of consciousness constituting the "subject's world".

Cognitively speaking, in a discource situation an expression perceived by the hearer is the object of his attention. After background noemata are made actual to resolve references, the perceived expression is interpreted, i.e. the partial world described in this expression is extented according to the hearer's own (situational, world, and word) knowledge. In the formalism of situation semantics this process is captured in the notion of interpretation. For [R\dot], [I\dot] denoting metavariables for R,I

Constraints are exactly the factors that determine the noetic structure of the consciousness. As formalized components of this structure, they are results of the feedback-driven evolution of a cognitive system or organism. In terms of existencial philosophy ( Heidegger 1927) this structure is a manifestation of being-in-the-world and in autopoietic terms ( Maturana/Varela 1980) it is a result of phylo- and ontogenetic structural coupling.

On the propositional level, noetic structures can be modelled as relations between abstract situations, i.e. event types. With any such relation being an autopoiesis-driven connection, focussing on the perceived expression will "automatically" generate its interpretation. The interpretation e of a situation e is thus defined as follows:

In terms of phenomenology, the set of all constraints determines an actual interpretation possible which is what Husserl called a "subject's world". As such, it cannot be characterized as a domain of external objects, which stands in contrast to a subject's internal domain; instead, the links between these two domains are to be thought of as pre-theoretical, constituting a (cognitive) system's interpretable world (Lebenswelt) whose abstractions only might result in the duality of categorial-type rationalistic mind-world or subject-object separation. In terms of cybernetics, this means that the traditional approach, i.e. modelling a subject, its surrounding environment and a feedback between them, will not do; instead, these two components merge to build an indecomposable model, which bears the characteristics of an autopoietic system³. This is the reason why we do not venture to model the meaning of an expression along reference-theoretical lines as range of a denotational function, but let it be derived procedurally as a dynamic description which represents the structural connections of an expression within its whole situational embedding constituting "its world". Such a description is the interpretation e whose formal properties are to be modelled in the sequel.

2 A topos theoretical model

áCOE,PERS ñ is a topological space. Every E Î ET can be thought of as a discrete topological space and every f Î ANCH as a local homeomorphism. If constraints CONS are formalized as topological mappings we have the structure overleaf.

This structure is a sheaf and sheaves build a topos. We call this topos SIT. The objects in SIT are the eventtypes together with corresponding anchors and the SIT-morphisms are constraints. The terminal object is áCOE, id_COE ñ and the germ of P Î PERS is | P | _{» _e}, where

The subobject classifier is È_e{áe, | P | _{» _e} ñ | P Î PERS }, so that the internal truth values are the open sets of COE, i.e. the persistent ones. So the SIT-formalism supports a phenomenological interpretation of situation semantics, since the "truth values" in SIT are exactly the possible world descriptions.

The procedural structure of topoi also allows for a formalization of meaningfulness (Bedeutsamkeit). If we consider SIT to be a model of the noetic structure, the interpretation of a situation can be captured in the following definition:

Since e contains all situations connected directly with it via the event types, and - since composition of morphisms is defined in SIT - also those indirectly connected with it, e is an individual extension of the world description expressed in e which reflects the noetic structure of the hearer. Thus, the immediate generation of interpretations is an expression of the structure as developed from structural coupling. SIT may therefore be understood as a semantic network with an internal logic varying according to changes both of the accessability and realm of situational attunement. In contrast to classical formalisms for knowledge representation which have been conceived as depicting some of the (inter)subjective reflections of entities which an external, objective world and reality would provide, SIT focusses on the basic structuredness which the communicative use of language in discourse by speakers/hearers will both, constitute and modify as a paradigm of cognition and a model of being-in-the-world.

Suppose we have a robot with an initial structure of constraints modelled as SIT-topos. Provided the robot is a cognitive system exposed to natural language discourse and capable of basic structural processing, then its (rudimentary) interpretations generated from given texts will not change its subsequent interpretations via altered input-cycles, but the system will come up with differing interpretations due to its modified old and/or established new constraints as structural properties of processing. Thus i is the structur that determines the system's interpretation which will be subject to changes constituting the robot's structural coupling.

[ ...] 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 learning⁴

In autopoietic terms, there would not be the same organism or cognitive system having acquired improved knowledge but a new system which is better adapted (attuned) to the surrounding world. Considering a text understanding system and letting a text be a sequence of situations, then the system - according to its own primary structuredness - will identify connections between situations whose recurrent structures in turn will modify the system in order to build up its autopoietic existence the principles of which are modeled here as topos.

A measure of mutual interrelationship between two eventtypes may be devised as the number of their common contexts. For E Î ET and ANCH_tot the set of total functions from ANCH is

with the elements of E¯ being its contexts. Now an inductive measure⁵ conf: ET ×ET ® [0,1] can be introduced:

with E+E¢ being the coproduct in SIT and conf being a real number between 0 and 1. If E¢ always co-occurs with E then conf(E,E¢) = 1 with conf being a correlational measure for the constraint c(E)=E¢. Learning for the robot cognitive system, therefore, is development of its topos structure according to computations of the conf measure whose values depend on the structures as exhibited by the texts processed.

The interpretation can now be extended in order to include not only the constrained situations but also their conf-values:

This (11) is an expression of the self-organizing structure which is a model of the noetic structure constituting the cognitive system's own "world".

3 The dispositional analysis

In terms of autopoietic systems, approaches to natural language semantics on the propositional level presuppose that the linguistic entities combined to form language expressions have independent meaning and can therefore be identified and interpreted in discourse. Although structural linguistics offeres some hints⁶ to how language items as linguistic entities come about to be employed the way they are, propositional approaches tend to assume that word meanings are somewhat static entities instead of variable results of processes constituted via semiotically different levels of abstraction whose modelling will have to be executed on different levels of description and analysis too.

Thus, complementing the independent sign-meaning view of information processing and the propositional approach in situation semantics, the contextual usage-meaning view in word semantics may open up new vistas in natural language processing and its semantic models ( Rieger 1989b).

Within the formal framework of situation semantics lexical items (as word-types) appear to render basic uniformities (as word-tokens) in any discourse whose syntagmatic or linear a n d paradigmatic or associative ⁷ relatedness can not only be formalized in analogy to topos theoretical constructions but also allows for the empirical analyses of these structures and their possible restrictions in order to devise mechanisms to model operational constraints.

For a vocabulary V = {x_n } of word-types, its set of ordered pairs as binary relation R, and a set of evaluating indixes I, V ×R ×I will denote the set of lexical situations. For P denoting possible locations - not of spatiotemporal homogeneity of an external world as in (1) - but of spatiotemporal, i.e. pragmatic homogeneity of discourse situations, the set of lexical course-of-events

represents the situational possibilities whose p-restriction isolates those members of LCOE_p Í LCOE which exhibit pragmatically conditioned constraints that any con- and cotextual embedding of word-tokens in a situation p Î P will provide.

Whereas (2) presupposes an external world for the truth-functional evaluation of described situations which a discourse situational interpretations of an expressions may offer in terms of persistent coes, (12) presupposes but the structuredness of communicative language discourse to let cognitive systems attuned (and coupled) to these structures identify (and modify) them in order to understand and convey meanings. As some of these structures can empirically be obeserved and numerically be specified, they allow for a systematic, quantitative reconstruction solely from large corpora of p-discourse revealing the type and degree of relatedness of persistent lcoe which apparently yield the semiotic base for possible interpretations in a discourse situation.

For linguistic events le, le¢ Î LCOE_p, the set of all possible, persistent LPER Í LCOE_p can formally be defined as

In terms of empirically accessible word-tokens in discourse from p-restricted situations, lper (let alone LPER) cannot, however, be collected directly from observable texts but has to be derived by analysing regularities on one level to induce structures on the other.

Based upon the distinction of the syntagmatic and paradigmatic structuredness of language items in discourse, the core of lper can be captured by a two-level process of abstraction (called a- and d-abstraction) providing the set of possible linguistic anchors and the sets of lexical eventtypes :

For a text corpus K = { t }, t = 1, ¼, T of p-restricted discourse, having an overall length L = å_t=1^T l_t ; 1_t £ l_t £ L measured by the number of word-tokens per text, and a vocabulary V = { x_n } ; n = 1,¼,i,j,k, ¼,N of word-types n whose frequencies are denoted by H_i = å_t=1^T h_it ; 1_it £ h_it £ H_i, the a-abstraction is based on a modified correlation-coefficient a_i,j that measures mutual (positive) affinity or (negative) repugnancy of pairs of word-tokens (x_i,x_j) Î V ×V

As a fuzzy binary relation, a: V ×V ® I can be conditioned on x_n Î V which yields a crisp mapping

where (x_i,a(i,1), ¼,a(i,N)) = y_i Î C represents the numerically specified, syntagmatic usage-regularities that have been observed for each word-type x_i against all other x_n Î V and can therefore be abstracted over one of the terms in each ordered pair thus defining an element y_i Î C.

Considering C as representational structure of abstract syntagmatic regularities, similarities and/or dissimilarities between them will capture paradigmatic regularities. This is achieved by the d-abstraction which is based on a numerically specified evaluation of differences between any two elements y_i,y_j Î C by

As a fuzzy binary relation, also d₁ : C ×C ® I can be conditioned on y_n Î C which again yields a crisp mapping

where (y_i,d₁(i,1), ¼, d₁(i,N)) = z_i Î S represents the numerically specified paradigmatic structure that has been derived for each abstract syntagmatic usage-regularity y_i against all other y_n Î C and can therefore be abstracted as in (17), this time, however, over the other of the terms in each ordered pair thus defining an element z_i Î S.

Identifying S with LET_p, the set of possible constraints LCON_p = LET_p ×LET_p may thus structurally be evaluated without (direct or indirect) recourse to any pre-existent external world described in the texts analysed

constituting a hyperstructure called semantic space áS,d₂ ñ. As LCON_d₂ is the set of possible constraints on combinations of elements z_n Î S = LET_p which are numerically specified in terms of d₂ as a metric on S, these specifications are used to make the procedurally defined let-selection operate.

The so-called D-operation has been conceived as an optimal spanning tree -al/-go/-rithm. The procedure is recursively defined to operate on the set of meaning points z_n Î áS,d₂ ñ. Given one meaning point's position as a start, the algorithm will work its way through all labeled points in the semantic space - unless stopped under conditions of a given target node, number of nodes to be processed, or threshold of maximal distance - transforming prevailing similarities of paradigms as represented by adjacency of points to induce a binary, non-symmetric, and transitive relation LCON_R of lexical relevance between them. This relation allows for the hierarchical reorganization of meaning points as nodes under a primed head in an n-ary tree called dispositional dependency structure (DDS) ( Rieger 1985).

Weighted numerically as a function of an element's distance values and its associated node's level and position in the tree, lcon_R(z_i) either is an expression of the head-node's z_i meaning-dependencies on the daughter-nodes z_n or, inversely, expresses their meaning-criterialities adding up to an aspect's interpretation determined by that head ( Rieger 1989a). To illustrate the feasibility of the D-operation's generative procedure, a set of relevant, linguistic constraints { lcon_R(z_i) } anchored with the lexical item x_i, i = UNTERNEHM/enterprise is shown in the format of a weighted⁸ semantic dispositional dependency structure according to the usages as detected from a corpus of German newspaper texts⁹.

References

Barwise, J. / Perry, J.(1983): Situations and Attitudes. Cambridge, MA (MIT)

Heidegger, M. (1927): Sein und Zeit. Tübingen (M.Niemeyer)

Husserl, E. (1976): Ideen II (Husserliana III/1), DenHaag (M. Nijhoff)

Maturana, H. / Varela, F. (1980): Autopoiesis and Cognition. Dordrecht (Reidel)

Peirce, C.S. (1906): "Pragmatics in Retrospect: a last formulation" (CP 5.11 - 5.13), in: The Philosophical Writings of Peirce. Ed. by J. Buchler, New York (Dover), p.269 - 289

Rieger, B. (1985): "Lexikal Relevance and Semantic Dispositions." in: Hoppenbrouwes/Seuren/Weijters (Eds.): Meaning and the Lexicon. Dordrecht (Foris), p.387 - 400

Rieger, B. (1989a): "Situations and Dispositions. Some formal and empirical tools for semantic analysis" in: Bahner, W. (Ed.): Proceedings of the XIV. Intern.Congress of Linguists (CIPL), Berlin (Akademie) [in print]

Rieger, B. (1989b): Unscharfe Semantik. Bern / Frankfurt / NewYork (P.Lang) [in print]

Rumelhart, D.E. / McClelland, J.L (1986): Parallel Distributed Processing. Explorations in the Microstructure of Cognition. 2 Vols. Cambridge, MA (MIT)

Varela, F. (1979): Principles of Biological Autonomy. NewYork (North Holland)

Wiener, N. (1956): The Human Use of Human Beings. Cybernetics and Society. New York (Doubleday Anchor)

Wittgenstein, L. (1958): The Blue and Brown Books. Ed. by R. Rhees, Oxford (Blackwell)

Footnotes:

¹to appear in: Retti, J./ Leidlmair, K. (Eds.): 5. Österreichische Artificial-Intelligence-Tagung, Igls/Tirol - Proceedings (Informatik Fachberichte 208), Berlin/Heidelberg/New York (Springer) 1989, pp. 365-375

² Barwise, J./ Perry, J.: Situations and Attitudes. Cambridge (MIT Press) 1983, p.16

³This is illustrated by the development of the notion of autopoiesis from homeostasis ( Varela 1979) and corroborates the idea of semiosis as a self-reflecting sign-constituting system ( Peirce 1906).

⁴ Wiener, N.: The Human Use of Human Beings. Cybernetics and Society. NewYork (Doubleday Anchor) 1956, p.60. - The distinction made conforms to back propagation in algorithmic models of learning mechanisms developed in connectionistic system architectures of parallel distributed processing (cf. Rumelhart, D.E. / McClelland, J.L. 1986).

⁵conf for confirmation

⁶In subscribing to the systems-view of natural languages, the distinction of langue-parole and competence-performance in modern linguistics allowes for different levels of language description. Being able to segment strings of language discourse and to categorize types of linguistic entities is to make analytical use of the structural coupling represented by natural languages as semiotic systems.

⁷According to the terminology of early linguistic structuralism as well as recent models in cognitive networking.

⁸Numerical values attached to nodes denoting distance /criteriality.

⁹Randomly assembled from first two pages of the daily DIE WELT, Jg.1964, Berlin edition.

Situations, Topoi, and Dispositions. On the phenomenological modelling of meaning1

Burghard B. Rieger, Constantin Thiopoulos Deptment of Computational Linguistics, FB II: LDV/CL - University of Trier Postf. 3825, D-5500 TRIER, West Germany