Pathology of collective doxa. Automata models

We use a conventional belief operator to derive a pentad of operators of kn owledge, misbelief, delusion, doubt and ignorance. The operators are consid ered to be states of agent belief, and are called, therefore, doxastic stat es. The binary composition of doxastic states is constructed and investigat ed. Some useful algebraic properties of the composition are highlighted. Se veral derivatives of the composition of doxastic states are analysed and as signed to the so-called naive, conservative, anxious and contradictory agen ts. The discrete dynamics of reflecting agents and stirred collectives of a gents is under study from the automata point of view. The non-stirred, or o rdered, collectives of agents exhibit in their evolution the richest range of space-time phenomena from the competing domains of regular patterns to t he random trees and triangles. They are analysed in detail, including possi ble influence of algebraic properties of doxastic compositions on space-tim e patterns of doxastic derivatives that emerge in the evolution of agent co llectives. 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. (C) 2001 Elsevier Science Inc. All rights reserved.