Fixpoint 3-Valued Semantics for Autoepistemic Logic

The paper presents a constructive 3-valued semantics for autoepistemic logic (AEL). Weintroduce a derivation operator and define the semantics as its least fixpoint. The semantics is 3-valued in the sense that, for someformulas, the least fixpoint does not specify whether they are believed or not. Weshowthat complete fixpoints of the derivation operator correspond to Moore’s stable expansions. In the case of modal representations of logic programsour least fixpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used). Weshow that, compurationally, our semantics is simpler than the semantics proposed by Moore (assuming that the polynomial hierarchy does not collapse).

Authors

• Marc Denecker
• Victor Marek Miroslaw Truszczynski

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