Translating Multi-Agent Autoepistemic Logic into Logic Program

Abstract

In order to develop a proof procedure of multi-agent autoepistemic Logic (MAEL), a natural framework to formalize belief and reasoning including inheritance, persistence, and causality, we introduce a method that translates a MAEL theory into a logic program with integrity constraints. It is proved that there exists one-to-one correspondence between extensions of a MAEL theory and stable models of a logic program translated from it. Our approach has the following advantages: (1) We can obtain all extensions of a MAEL theory if we compute all stable models of the translated logic program. (2) We can fully use efficient techniques or systems for computing stable models of a logic program. We also investigate the properties of reasoning in MAEL through this translation. The fact that the extension computing problem can be reduced to the stable model computing problem implies that there are close relationships between MAEL and other formalizations of nonmonotonic reasoning.