Abstract :
The paper aims to investigate influences of norms on a space-time dynamic of stirred (solutions) and non-stirred (lattices) collectives of very simple believing agents. A mental state of an agent is characterized by agentʹs belief in some proposition and a truth value of the proposition in agentʹs local vicinity. Every agent of the collective updates its belief depending on its current belief, belief of its closest neighbours and truth value of the proposition in neighbourhood of the neighbours. Each agent is represented by a finite automaton – a so-called doxaton [A. Adamtzky, Appl. Math. Comput., in press]. The doxaton takes five doxastic states, derived from the belief: knowledge, doubt, misbelief, delusion and ignorance. In the above mentioned reference, we defined a binary composition of doxastic states and investigated its algebraic structure. The composition itself is not deterministic; however, it can be made deterministic by applying norms. The norms are expressed in a priority order on the doxastic states. Space-time evolution of the solutions and the lattices of doxatons is studied in computer experiments to understand influences of norms and initial conditions on the behaviour of abstract collectives of simple agents. Diffusion and reaction of doxastic states are explored as well as formation of stationary patterns of the doxastic states.
