Reliable Semantics for Extended Logic Programs with Rule Prioritization

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Abstract
We present a new semantics for extended logic programs with rule prioritization (EPP). The semantics, called reliable semantics (RS), generalizes the well-founded semantics which is defined for normal programs. It also generalizes the extended well-founded semantics which is defined for non-contradictory extended programs. Because of the classical negation in the head of the rules, the well-founded model of a program can be contradictory. RS is contradiction-free and defined for all EPPs. To avoid contradictions, only reliable rules and reliable closed world assumptions are used in the fixpoint computation of RS. A closed world assumption (CW A) is considered reliable if it is not ‘suspect’ for any constraint violation. A rule r is considered reliable if it is not ‘suspect’ for any constraint violation caused by rules with priority no lower than r. We define the stable r-models of an EPP and we show that the RS of a program coincides with its least stable r-model. The RS of an EPP, P, represents the skeptical ‘meaning’ of P whereas stable r-models of P represent the possible ‘meanings’ of P.

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