A Descriptive Approach to Preferred Answer Sets

Abstract

We are aiming at a semantics of logic programs with preferences defined on rules, which always selects a preferred answer set, if there is a non-empty set of (standard) answer sets of the given program.It is shown in a seminal paper by Brewka and Eiter that the goal mentioned above is incompatible with their second principle and it is not satisfied in their semantics of prioritized logic programs. Similarly, also according to other established semantics, based on a prescriptive approach, there are programs with standard answer sets, but without preferred answer sets.According to the standard prescriptive approach no rule can be fired before a more preferred rule, unless the more preferred rule is blocked. This is a rather imperative approach, in its spirit. According to our background intuition, rules can be blocked by more preferred rules, but the rules which are not blocked are handled in a more declarative style, independent on the given preference relation on the rules.An argumentation framework (different from Dung’s framework) is proposed in this paper. Some argumentation structures are assigned to the rules of a given program. Other argumentation structures are derived using a set of derivation rules. Some of the derived argumentation structures correspond to answer sets. An attack relation on derivations of argumentation structures is defined. Preferred answer sets correspond to complete argumentation structures, which are not blocked by other complete argumentation structures.