Translating Multi-Agent Autoepistemic Logic into Logic Program

Abstract

In this paper, we develop a proof procedure for multi-agent autoepistemic logic (MAEL) by translating it into a logic program with stable model semantics. We introduce a method that translates a MAEL theory in normal form into a logic program which includes integrity constrains, and prove some theorems that guarantee soundness and completeness of the translation. In fact, there is a one-to-one correspondence between MAEL extensions of a theory and stable models of a logic program which is translated from the theory. Our approach has the following advantages compared with the former ones whose decision procedures are based on tableaux and resolution technique: (1) We can get all extensions (all inference results) of a MAEL theory if we compute all stable models of the logic program. (2) We can fully use efficient techniques or systems for computing stable models of a logic program on the process of MAEL theorem proving. Furthermore, we investigate properties of inference on MAEL through this translation. The fact that the extension computing problem of MAEL can be reduced to a stable model computing problem of logic programs implies that there are close relationships between MAEL and other formalizations of nonmonotonic reasoning.