Disjunction In Resource-Oriented Deductive Planning

To model in a formal system the remarkable ability of human agents to reason about situations , actions, and causality has always been a major research goal in Intellectics. Most of the work towards this goal is based on the situation calculus which, however, has the disadvantage that it requires either to state frame axioms or to use nonmonotic logic and a commonsense law of inertia. Recently, three new deductive approaches were developed which do not show this disadvantage. These are the linear connection method, an equational Horn logic, and the linear logic. Their key idea is to treat facts about a situation as resources which can be consumed and produced by actions. The approaches are essentially equivalent for conjunctive planning problems, ie. problems, where situations and conditions as well as eeects of actions are (non-idempotent) conjunctions of facts. In this paper we extend and revise the equational logic approach and the linear connection method to handle also disjunctions of facts. We show that these extended approaches and the approach based on linear logic augmented by rules handling disjunction are equivalent wrt. a unique semantic of disjunctive planning problems.