Preferred Answer Sets for Ordered Logic Programs

TL;DR

This paper extends answer set semantics to handle inconsistent logic programs by introducing preferred answer sets based on rule preferences, enabling better modeling of real-world scenarios like database repairs.

Contribution

It introduces a novel semantics for ordered logic programs that incorporates rule preferences to identify preferred answer sets, enhancing expressiveness and practical applicability.

Findings

Preferred answer sets are minimal elements under a rule-based order.

The semantics can simulate negation as failure and disjunction.

Application to database repair demonstrates practical utility.

Abstract

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets. To appear in Theory and Practice of Logic Programming (TPLP).