Warranted Derivations of Preferred Answer

TL;DR

This paper introduces a new semantics for logic programs with preferences, using an argumentation framework to better handle preferred answer sets in a more declarative manner.

Contribution

It proposes a novel argumentation-based semantics that allows non-blocked rules to be handled declaratively, improving over existing imperative approaches.

Findings

The new semantics guarantees the existence of preferred answer sets when standard answer sets exist.

It provides a formal framework for deriving preferred answer sets via argumentation structures.

The approach differs from traditional semantics by allowing non-blocked rules to be handled independently.

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. In our approach, rules can be blocked by more preferred rules, but the rules which are not blocked are handled in a more declarative style, their execution does not depend on the given preference relation on the rules. An argumentation framework (different from the Dung's framework) is proposed in this paper. Argu- mentation structures are derived from the rules of a given program. An attack relation on argumentation structures is defined, which is derived from attacks of more preferred rules against the less preferred rules. Preferred answer sets correspond to complete argumentation structures, which are not blocked by other complete argumentation structures.