Brain and Its Universal Logical Model of Multi-Agent Biological Systems

Abstract

AbstractWe build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as Physarum polycephalum, bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the topological description of brain activity, where particles (neurons) are activated by an external environment, represented by a topological space X with an open cover $$\{U_i:i\in I\}$$ { U i : i ∈ I } . The brain builds the model of this external space via the nerve (trace) of a topological space X. Here the body of Physarum polycephalum or a swarm made of networks of tubular structures represents a nerve (trace) of X also which means that Physarum polycephalum or a swarm gains orientation in the space of external stimuli even in the absence of any neural system. The logic of living organisms is based on open subsets of X and thus can be represented by Heyting algebra (i.e. intuitionistically). We also consider the generalisation of the nerve construction to a categorical context, where the category is determined by the network structures of multi-agent biological system. This model can be generalised up to simulating the behaviour of any swarm by means of intuitionistic logic.