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Victor Marek

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AIJ Journal 2002 Journal Article

Annotated revision programs

Victor Marek
Inna Pivkina
Mirosław Truszczyński

Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence (probability) that a revision atom holds. The main goal of our paper is to reexamine the work of Fitting, argue that his semantics does not always provide results consistent with intuition, and to propose an alternative treatment of annotated revision programs. Our approach differs from that proposed by Fitting in two key aspects: we change the notion of a model of a program and we change the notion of a justified revision. We show that under this new approach fundamental properties of justified revisions of standard revision programs extend to the annotated case.

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AAAI Conference 1998 Conference Paper

Fixpoint 3-Valued Semantics for Autoepistemic Logic

Marc Denecker
Victor Marek

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).

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