The Boundary between Decidable and Undecidable Fragments of the Fluent Calculus

Abstract. We consider entailment problems in the fluent calculus as they arise in reasoning about actions. Taking into account various fragments of the fluent calculus we formally show decidability results, establish their complexity, and prove undecidability results. Thus we draw a boundary between decidable and undecidable fragments of the fluent calculus. 1 Introduction Intelligent agents need to reason about the state of the world, the actions that they can perform and the effects that are achieved by executing actions. To elaborate on the question whether there exists a sequence of actions such that a given goal can be achieved by executing this sequence in the current state is one of the most important tasks an intelligent agent has to perform. From a logical point of view this amounts in solving an entailment problem as already laid down in [18]. Likewise, many other problems in reasoning about actions can be formalized as entailment problems in a suitable logic