Belief Revision of Logic Programs under Answer Set Semantics

James P. Delgrande, Torsten Schaub, Hans Tompits, Stefan Woltran

We address the problem of belief revision in (nonmonotonic) logic programming under answer set semantics: given logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. Unlike previous approaches in logic programming, our formal techniques are analogous to those of distance-based belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic characterisation of logic programs, we can adapt well-known techniques from the area of belief revision to revision in logic programs We investigate two specific operators: (logic program) expansion and a revision operator based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical AGM-style belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy the majority of the AGM postulates for revision. A complexity analysis reveals that our revision operators do not increase the complexity of the base formalism. As a consequence, we present an encoding for computing the revision of a logic program by another, within the same logic programming framework.

Subjects: 15.1 Belief Revision; 3.3 Nonmonotonic Reasoning

Submitted: Jun 17, 2008

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