The common ground and widely accepted frame for modelling the semantics of natural language is to be found in the dualism of the rationalistic tradition of thought as exemplified in its notions of some independent (objective) reality and the (subjective) conception of it. According to this realistic view, the meaning of a language term (i.e. text, sentence, phrase, word, syllable) is conceived as something being related somehow to (and partly derivable from) certain other entities, called signs, a term is composed of. As a sign and its meaning is to be related by some function, called interpretation, language terms, composed of signs, and related meanings are understood to form some structures of entities which appear to be at the same time part of the (objective) reality and its (subjective) interpretation of it. In order to let signs and their meanings be identified as part of language terms whose interpretations may then be derived, some knowledge of these structures has to be presupposed and accessible for any symbolic information processing. Accordingly, understanding of language expressions can basically be identified with a of matching some input strings with supposedly predefined configurations of word meaning and/or world structure whose representations have to be available to the (natural or artificial) understanding system's particular (though limited) knowledge. The so-called cognitive paradigm of advanced procedural linguistics can easily be traced back to stem from this fundamental duality, according to which natural language understanding can be modelled as the knowledge-based processing of information.
Subscribing to this notion of understanding, however, tends to be tantamount to accepting certain unwarranted presuppositions of theoretical linguistics (and particularly some of its model-theoretical semantics) which have been exemplified elsewhere1 by way of the formal and representational tools developed and used so far in cognitive psychology (CP), artificial intelligence (AI), and computational linguistics (CL). In accordance with these tools, word meaning and/or world knowledge is uniformly represented as a (more or less complex) labelled graph with the (tacid) understanding that associating its vertices and edges with symbols from some established system of sign-entity-relationship (like e.g. that of natural language) will render such graph-theoretical configurations a model of structures or properties which are believed to be those of either the sign-system that provided the graphs' labels or the system of entities that was to be depicted. Obviously, these representational formats are not meant to model the emergence of structures and the processes that constitute such structures as part of word meaning and/or world, but instead are merely making use of them2.
In following a semiotic paradigm this inadequacy can be overcome, hopefully allowing 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 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, stayed (or be kept) out of the focus of interest, or were being overlooked altogether, sofar. Moreover, there is some chance to bridge the gap between the formal theories of language description ( competence) and the empirical analysis of language usage (performance) that is increasingly felt to be responsible for some unwarranted abstractions of fundamental properties of natural languages.
Approaching the problem from a cognitive point-of-view, identification and interpretation of external structures has to be conceived as some form of information processing which (natural/artificial) systems-due to their own structuredness-are (or ought to be) able to perform. These processes or the structures underlying them, however, ought to be derivable from-rather than presupposed to-procedural models of meaning4. Based upon a phenomenological reinterpretation of the analytical concept of situation as expressed by Barwise/Perry (1983) and the synthetical notion of language game as advanced by the late Wittgenstein (1958), the combination of both lends itself easily to operational extensions in empirical analysis and procedural simulation of associative meaning constitution which may grasp essential parts of what Peirce named semiosis 5.
Modelling the meaning of an expression along reference-theoretical lines had to presuppose the structured sets of entities to serve as range of the denotational function which provided the expression's interpretation. However, it appears feasible to have this very range be constituted as a result of exactly those cognitive functions by way of which understanding is produced. It will have to be modelled as a dynamic generation which reconstructs the possible structural connections of an expression towards cognitive systems (that may both intend/produce and realize/understand it) and in respect to their situational settings, being specified by the expressions' pragmatics.
In phenomenological terms, the set of structural constraints defines any cognitive (natural or artificial) system's possible range in constituting its schemata whose instantiations will determine the system's actual interpretations of what it perceives. As such, these cannot be characterized as a domain of objective entities, external to and standing in contrast with a system's internal, subjective domain; instead, the links between these two domains are to be thought of as ontologically fundamental 6 or pre-theoretical. They constitute-from a semiotic point-of-view-a system's primary means of access to and interpretation of what may be called its ''world'' as the system's particular apprehension of its environment. Being fundamental to any cognitive activity, this basal identification appears to provide the grounding framework which underlies the duality of categorial-type rationalistic mind-world or subject-object separation.
From a systems-theoretical point-of-view, this is tantamount to a shift from linear to non-linear systems in modelling cognitive and semiotic behaviour. The simplest way to distinguish these approaches is by identifying the behaviour of linear systems as being equal to the sum of the behaviour of its parts, whereas the behaviour of non-linear systems is more than than the sum of its parts. Freges principle of compositionality as well as Chomskeys hypotheses of independance of syntax are concepts in point of the linear -systems'-view: by studying the parts of a system in isolation first, will then allow for a full understanding of the complete system by composition. This collides with the non-linear -systems'-view according to which the primary interest is not in the behaviour of parts as properties of a system but rather in the behaviour of the interaction between parts of a system. Such interaction-based properties necessarily disappear when the parts are studied in isolation, as can be witnessed in referencial and model-theoretic semantics where phenomena like vagueness, contextual variability and creative dynamism cannot be dealt with, or in competence theoretical syntax where grades of grammaticality, adaptive change and discourse adequacy cannot be addressed.
The self-organizing property of the non-linear system introduced here has formally been derived elsewhere7 from mathematical topos theory 8 and category theory 9. This implementation of the system and its organisation as a dynamic hypertext structure is to simulate the emergence of lexical meanings by way of word co-occurrence constrains of-as yet-rather coarse syntagmatic/paradigmatic regularities in natural language texts.
A full subcategory is thus a subcategory that contains all the morphisms of the original category between its objects, i.e. it is a function closed under functional application.
A special class of categories is the class of cartesian closed categories. They are characterized by the fact that some structural operation are defined of them. Here we consider two of them:
The nodes of the graph are the objects and the links the morphisms. For f:a ® b, a is the domain of f and b the codomain. comp is the (associative) composition of morphisms and id maps each object to the corresponding identity morphism.
The transformation of the matrix CONF to a category C(CONF) is defined by:
The meaning of a lexem a, as a structural description of how a is interlinked in the network of lexems, according to a numerical boundary GLB that determines the depth of the activation, is given by:
The meaning of two or more lexems can be represented as a full subcategory generated by the product and coproduct constructions.
A situation is thus a substructure of the original category that is closed under functional application and since it is a category again it is possible to apply the same mechanisms as in the original category. The meaning of a lexem a relative to a situation, SIT(b,c) is a* in SIT(b,c).
Each object of C(CONF) is implemented as a card named after this object that contains a text field with the name (see figure 3). Each morphism f:a ® b is implemented as a button on the card named a that leads, when activated, to the card named b. The name of the button is formed by concatenating b with conf(f) (see figure 3). The user can navigate through the network by clicking on the buttons. The structural operations defined on C(CONF) can be implemented as browsers and the determined portions of the network can be accessed via hyperviews.
These mechanisms can be activated by clicking on the buttons of the control card:
The process of restricting the category C(CONF) can be used recursively and reflects the focus of interest of the user of the system. In this example (that, since it corresponds to the first stages of the system has a rough structure) the view of the category C(CONF) is given in figure 5 and the view of the full subcategory sit(industrie,technik) is given in figure 6. The text field in figure 6 contains the lexems that led to this view and for successive determinations of situations, i.e. situations of situations of ..., it contains the history of the restrictions. By using the Interpret button of the hypertext file that represents the actual situation the user can determine the meaning of a lexem relative to this situation.
Barrett, E. (Ed.)(1988): Text, ConText, and HyperText. Cambridge, MA (MIT) Barwise, J./ Perry, J.(1983): Situations and Attitudes. Cambridge, MA (MIT) Bell, J. L. (1981): "Category theory and the foundation of mathematics" British Journal of the Philosophy of Science, 32,1981:349-358 Conklin,J. (1987): "Hypertext: an introduction and survey" Computer, Vol.20, No.9. Frisse, M. (1987): "From text to hypertext" Byte October, 1987. Goldblatt, R. (1984): Topoi. The Categorial Analysis of Logic. (Studies in Logic and the Foundations of Mathematics 98), Amsterdam (North Holland) Heidegger, M. (1927): Sein und Zeit. Tübingen (M.Niemeyer) Lambek, J./ Scott P. J. (1986): Introduction to higher order categorical logic. Cambridge (Cambridge University Press) Maturana, H./ Varela, F. (1980): Autopoiesis and Cognition. The Realization of the Living. 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), pp. 269-289 Rieger, B. (1977): "Bedeutungskonstitution. Einige Bemerkungen zur semiotischen Problematik eines linguistischen Problems" Zeitschrift für Literaturwissenschaft und Linguistik 27/28, pp. 55-68 Rieger, B. (1985b): "On Generating Semantic Dispositions in a Given Subject Domain" in: Agrawal, J.C./ Zunde, P. (Eds.): Empirical Foundation of Information and Software Science. New York/ London (Plenum Press), pp. 273-291 Rieger, B. (1989): Unscharfe Semantik. Die empirische Analyse, quantitative Beschreibung, formale Repräsentation und prozedurale Modellierung vager Wortbedeutungen in Texten. Frankfurt/ Bern/ New York (P. Lang) Rieger, B. (1990): "Situations and Dispositions. Some formal and empirical tools for semantic analysis" in: Bahner, W. / Schildt, J./ Viehweger, D. (Ed.): Proceedings of the XIV.International Congress of Linguists (CIPL), Vol. II, Berlin (Akademie Verlag), pp. 1233-1235 Rieger, B. (1991): "On Distributed Representation in Word Semantics" (ICSI-Report TR-91-012) International Computer Science Institute, Berkeley, CA Rieger, B.B./ Thiopoulos, C. (1989): Situations, Topoi, and Dispositions. On the phenomenological modelling of meaning. in: Retti, J./ Leidlmair, K. (Eds.): 5th Austrian Artificial Intelligence Conference. (ÖGAI 89) Innsbruck; (KI-Informatik-Fachberichte Bd.208) Berlin/ Heidelberg/ New York (Springer), pp. 365-375 Thiopoulos, C. (1991): Meaning metamorphosis in the semiotic topos. Theoretical Linguistics [in print] Winograd,T./ Flores, F. (1986): Understanding Computers and Cognition: A New Foundation for Design. Norwood, NJ (Ablex) Wittgenstein, L. (1958): The Blue and Brown Books. Ed. by R. Rhees, Oxford (Blackwell)
*Published in: Köhler, R./Rieger, B.B. (Eds.): Contributions to Quantitative Linguistics. Dordrecht/Boston (Kluwer), 1993, pp. 67 - 78.
**partly by support of The German Marshall Fund of the United States
1Rieger 1991
2For illustrative examples and a detailed discussion see Rieger 1989, pp. 103-132.
3see however Rieger (1977)
4It has been argued elsewhere (Rieger 1990, 1991) that meaning need not be introduced as a presupposition of semantics but may instead be derived as a result of semiotic modelling.
5''By semiosis I mean [... ] an action, or influence, which is, or involves, a cooperation 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)
6Heidegger (1927)
7Thiopoulos 1992 forthcoming
8Goldblatt 1979
9Bell 1981; Lambek/Scott 1986
10For a complete description of the theoretical framework see (Thiopoulos,1991).
11The implementation is made in Hypercard