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Cognitive Morphodynamics

Dynamical Morphological Models of Constituency in Perception and Syntax

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Jean Petitot

This book – written in collaboration with René Doursat, director of the Complex Systems Institute, Paris – adds a new dimension to Cognitive Grammars. It provides a rigorous, operational mathematical foundation, which draws from topology, geometry and dynamical systems to model iconic «image-schemas» and «conceptual archetypes». It defends the thesis that René Thom’s morphodynamics is especially well suited to the task and allows to transform the morphological structures of perception into Gestalt-like, abstract, proto-linguistic schemas that can act as inputs into higher-level specific linguistic routines.
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.

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Chapter 3. Relations 119

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CHAPTER 3 Relations In collaboration with Rene´ Doursat 1. Introduction How can the same English relationship ‘in’ apply to scenes as different as “the shoe in the box” (small, hollow, closed volume), “the bird in the tree” (large, dense, open volume) or “the fruit in the bowl” (curved surface)? What is the common ‘across’ invariant behind “he swam across the lake” (smooth trajectory, irregular surface) and “the fly zigzagged across the hall” (jagged trajectory, regular volume)? How can language, especially its spatial elements, be so insensitive to wide topological and morphological differences among visual percepts? In short, how does language drastically simplify information and categorize? The previous chapter addressed the basic concept of things and introduced algorithms dealing with image segmentation, perceptual mereology and object constituency. We now turn to the second major component of Langacker’s trilogy, the relations between things. Relations clearly constitute the most important problem at the core of all theories of language. Ultimately, different theoretical perspectives on syntax will be distinguished on the basis of how they construe relations. It is only after relations are expressed in a mathematical form that processes can be modeled as temporal evolutions of relations and events as changes occurring during these processes. 1.1. The gestaltic conception of relations The various theoretical paradigms of language are broadly divided between formal or symbolic conceptions of things and relations, on the one hand, and what we here call “gestaltic” conceptions, on the other hand. In the formal framework, things are...

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