A probabilistic approach to automaton-environment systems
Ivan Kramosil · Czech digital mathematics library · 1975
There are many papers dealing with the automaton-environment systems from deterministic point of view.The aim of this paper is to introduce a probabilistic aspect into this field.The presented model supposes that the actions of the automaton can involve certain unexpected consequences in the environment.Frame axioms are in this model replaced by a new deduction rule allowing to assume that some assertion, describing the situation of the environment in a past situation is valid also in the present situation under the condition that no explicit information about changes concerning this assertion is at disposal.It is proved that there is a positive probability that the system of assertions the aim of which is to describe the situation in the environment will become inconsistent.Using the apparatus of random walks we are able to prove that under certain conditions this probability of inconsistency tends to one when the number of actions performed by the automaton increases.