Game Semantics and Linear Logic in the Cognition Process

Abstract

A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment. The set has a lattice structure and a monoid structure; thus, the structure of linear logic is defined on the set. The cognition process of some environment by the system is described on this basis. The environment is represented as a configuration space of possible system positions which are estimated by an information amount (by corresponding sets). This information is supplied to the system by the environment. Thus, it is possible to define the category of Conway games with a payoff on the configuration space and to choose an optimal system's play (i.e., a trajectory). The choice is determined by the requirement of maximal information increasing and takes into account the structure of the system goal set: the linear logic on the set is used to determine the priority of possible different parallel processes. The survey may be useful to describe the behavior of robots and simple biological systems, e.g., ants.