Non-Markovian Control in the Situation Calculus

Alfredo Gabaldon

Abstract: The property that the executability and the effects of an action are determined entirely by the current state or situation is known as the Markov property and is assumed in most formalizations of action. It is not difficult, however, to run into scenarios when the Markov property is not present. We consider removing this assumption from the situation calculus based formalization of actions of Reiter, which forms the basis of the programming language Golog, and define an operator for regressing formulas that quantify over past situations, with respect to such nonMarkovian basic action theories.