Dynamical systems and cognitive linguistics: toward an active morphodynamical semantics.

We propose a novel dynamical system approach to cognitive linguistics based on cellular automata and spiking neural networks. How can the same relationship 'in' apply to containers as different as 'box', 'tree' or 'bowl'? Our objective is to categorize the infinite diversity of schematic visual scenes into a small set of grammatical elements and elucidate the topology of language. Gestalt-inspired semantic studies have shown that spatial prepositions such as 'in' or 'above' are neutral toward the shape and size of objects. We suggest that this invariance can be explained by introducing morphodynamical transforms, which erase image details and create virtual structures or singularities (boundaries, skeleton), and call this paradigm 'active semantics'. Singularities arise from a large-scale lattice of coupled excitable units exhibiting spatiotemporal pattern formation, in particular traveling waves. This work addresses the crucial cognitive mechanisms of spatial schematization and categorization at the interface between vision and language and anchors them to expansion processes such as activity diffusion or wave propagation.