A Family of Descriptive Approaches To Preferred Answer Sets

TL;DR

This paper introduces two new purely declarative methods for handling preferences in answer set programming, addressing conflicts effectively while maintaining desirable computational properties.

Contribution

It presents two novel declarative approaches for preference handling in logic programming that satisfy Principle I and work for general conflicts, including indirect ones.

Findings

First approach ignores preferences between non-conflicting rules.

Second approach maintains NP complexity and allows transformation to standard logic programs.

The approaches form a hierarchy with existing methods and solve a specific application problem.

Abstract

In logic programming under the answer set semantics, preferences on rules are used to choose which of the conflicting rules are applied. Many interesting semantics have been proposed. Brewka and Eiter's Principle I expresses the basic intuition behind the preferences. All the approaches that satisfy Principle I introduce a rather imperative feature into otherwise declarative language. They understand preferences as the order, in which the rules of a program have to be applied. In this paper we present two purely declarative approaches for preference handling that satisfy Principle I, and work for general conflicts, including direct and indirect conflicts between rules. The first approach is based on the idea that a rule cannot be defeated by a less preferred conflicting rule. This approach is able to ignore preferences between non-conflicting rules, and, for instance, is equivalent with the answer set semantics for the subclass of stratified programs. It is suitable for the scenarios, when developers do not have full control over preferences. The second approach relaxes the requirement for ignoring conflicting rules, which ensures that it stays in the NP complexity class. It is based on the idea that a rule cannot be defeated by a rule that is less preferred or depends on a less preferred rule. The second approach can be also characterized by a transformation to logic programs without preferences. It turns out that the approaches form a hierarchy, a branch in the hierarchy of the approaches by Delgrande et. al., Wang et. al., and Brewka and Eiter. Finally, we show an application for which the existing approaches are not usable, and the approaches of this paper produce expected results.