A Goal-Directed Procedure for an Extension Membership Problem in Arbitrary Propositional Default Theories

抄録

Default Logic is one of the most popular formalizations of nonmonotonic reasoning and a subclass of defaults called normal defaults has been used to formalize commonsense reasoning. Recent research such as Yale shooting problem, however, has revealed that the usage of arbitrary defaults is necessary for some commonsense reasoning. Although there are correct goal-directed procedures for normal default theories and some other restricted classes of default theories, no one has yet proposed any goal-directed proof procedure for a full class of arbitrary defaults even in a propositional case. In this paper, we present a correct goal-directed proof procedure for the extension membership problem of arbitrary consistent propositional default theories. This procedure is obtained by extending our previous procedure for general (abductive) logic program with integrity constraints so that clauses instead of atoms can be used in a head or a body of rules. Moreover, this procedure is complete if a default theory is finite. We also show that this procedure can be used for consistency checks of addition of rules.