Dynamical Morphological Models of Constituency in Perception and Syntax
Cognitive Grammars have drawn upon the view that the deep syntactic and semantic structures of language, such as prepositions and case roles, are grounded in perception and action. This study raises difficult problems, which thus far have not been addressed as a mathematical challenge. Cognitive Morphodynamics shows how this gap can be filled.
Conclusion In his paper A Suggestion for a Linguistics with Connectionist Foundation , George Lakoﬀ generalized Regier’s idea (see Section 5.3 of Chapter 3) to the conjecture that Ullman-style visual routines (...) are suﬃcient to characterize all known structures in cognitive topology. We think that we have demonstrated Lakoﬀ-Regier’s conjecture for actantial relations and interactions. Starting from the Smolensky/Fodor-Pylyshyn debate concerning connec- tionist modeling of constituency, we ﬁrst stressed that the main problem was to achieve a connectionist conﬁgurational deﬁnition of semantic (actantial) roles, that is, according to Jerry Fodor and Zenon Pylyshyn, of that “geometrical whole, where the geometrical relations are themselves semantically signiﬁcant”, and which constitutes the geometrical basis of constituent-structures. We have then emphasized that, in order to solve this non-trivial problem, we ﬁrst need a “good” linguistic theory. We selected cognitive grammars in Langacker’s, Talmy’s, Jackendoﬀ’s and Lakoﬀ’s sense and we stressed the cen- tral role of the localist hypothesis. Using this general perceptual, iconic and schematic grounding of basic elementary syntactic structures, we reduced the main problem to “perceptual” constituency. We then introduced contour diﬀusion/propagation routines that generalize, to higher-order representational levels, well-known routines of computational vision. We treated two cases of spreading activation triggered by boundaries: contour diﬀusion (heat equation) and contour propagation (wave equation). In these two cases we showed, according to deep theorems such as Morse’s theo- rem, that the singularities of the diﬀusion/propagation processes are singular structures that can be locally and...
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