Pathology of collective doxa. Automata models

摘要

We use a conventional belief operator to derive a pentad of operators of knowledge, misbelief, delusion, doubt and ignorance. The operators are considered to be states of agent belief, and are called, therefore, doxastic states. The binary composition of doxastic states is constructed and investigated. Some useful algebraic properties of the composition are highlighted. Several derivatives of the composition of doxastic states are analysed and assigned to the so-called naive, conservative, anxious and contradictory agents. The discrete dynamics of reflecting agents and stirred collectives of agents is under study from the automata point of view. The non-stirred, or ordered, collectives of agents exhibit in their evolution the richest range of space-time phenomena from the competing domains of regular patterns to the random trees and triangles. They are analysed in detail, including possible influence of algebraic properties of doxastic compositions on space-time patterns of doxastic derivatives that emerge in the evolution of agent collectives. We determine products of so-called interacting doxastic worlds, where every world is an element of a Boolean of the set of doxastic states, to enforce our insight in domains of attracting and impossible worlds.