Semantics and Communication for Memory Evolutive Systems

Abstract

In a series of preceding papers, the authors have developed the theory of Memory Evolutive Systems which represents a mathematical model (based on Category theory) for natural open self-organizing systems, such as biological, sociological or neural systems. In these systems, the dynamics is modulated by the cooperative or/and competitive interactions between the global system and a net of internal more or less specialized Centers of Regulation (CR) with a differential access to a central hierarchical Memory. Each CR operates at its own complexity level and time-scale, but their strategies are competitive, whence a 'dialectics between heterogeneous CRs which is at the root of higher order cognition. The problem tackled in the present paper is the emergence of a Semantics in the MES modeling a cognitive system; it relies on the detection of specific invariances by the CRs that leads to classify objects according to their main attributes, and form new formal units representing their invariance classes. The idea is that a (lower) CR, say E, classifies two objects B and C as having 'the same shape' if they activate the same pattern of its actors; however this classification remains implicit for E itself and it can be apprehended only by a higher Ievel CR which may memorize the invariance class by a higher object, called a 'E-concept'. The concepts with respect to the various CRs form the semantic memory which gives more flexibility in the evaluation, selection and memorization of appropriate strategies, as well as in internal or external communications.