Fixpoint 3-Valued Semantics for Autoepistemic Logic

The paper presents a constructive 3-valued semantics for autoepistemic logic (AEL). We introduce a derivation operator and de ne the semantics as its least xpoint. The semantics is 3-valued in the sense that, for some formulas, the least xpoint does not specify whether they are believed or not. We show that complete xpoints of the derivation operator correspond to Moore's stable expansions. In the case of modal representations of logic programs our least xpoint semantics expresses both well-founded semantics and 3-valued Fitting-Kunen semantics (depending on the embedding used). We show that, computationally, our semantics is simpler than the semantics proposed by Moore (assuming that the polynomial hierarchy does not collapse).

• Type: Conference
• Year: 1998
• Where: AAAI
• Authors: Marc Denecker, V. Wiktor Marek, Miroslaw Truszczynski
• Keywords: AAAI 1998, Constructive 3-valued Semantics, Derivation Operator, Intelligent Agents, Semantics