Logic of basic swarm reactions

Abstract

Abstract In the paper, there are defined continuous-valued logical functions defined on [0, 1] as natural reactions of swarm to several stimuli detected at one time step. In this model, the logical duality represented by squares or cubes of opposition is realizable by own swarm patterns based on lateral inhibition and lateral activation. Swarm reactions are considered not certain, but with a probability of their intensity in respect to the distance to an appropriate biologically active substance. At the same time, we can formalize cases when the swarm members are partly inhibited and partly activated. In other words, we assume that they can be less or more inhibited and less or more activated, etc. So, we can deal with a fuzzy mix of conjunction and disjunction at one time.