Embedding prioritized circumscription in disjunctive logic programs

Abstract

In this paper, we present a method for embedding prioritized circumscription of a clausal theory into general disjunctive logic programs (GDP) with negation as failure in the head. In recent works, Sakama and Inoue show that parallel circumscription can be embedded in GDP. They also show that prioritized circumscription of a clausal theory can be represented in the framework of GDP extended with priorities. Wang et al. recently have also shown that prioritized circumscription can be expressed in their priority logic by applying monotonic inference rules constrained by a priority relation among the rules. In our method, the priorities of minimization in the circumscription policy are translated into the syntactical form of logic program rules, and the models of the circumscription are precisely captured by the stable models of the program. Thus we show that prioritized circumscription can be directly embedded in GDP without extending the GDP logic programming framework. This result further asserts the expressive power of the class of general disjunctive programs and supports its use for knowledge representation in Artificial Intelligence. The results of this paper also lead to embeddings of prioritized circumscription into the MBNF logic of Lifschitz and AE logic of Moore.