Cost-Based Semantics for Querying Inconsistent Weighted Knowledge Bases

TL;DR

This paper introduces a cost-based semantics framework for querying inconsistent weighted description logic knowledge bases, enabling more nuanced reasoning by considering interpretation costs and optimality.

Contribution

It provides a comprehensive analysis of the complexity of querying under cost-based semantics for a range of description logics, extending previous qualitative approaches.

Findings

Complexity results for bounded cost satisfiability

Complexity analysis for certain and possible answer recognition

Applicability to description logics between ELbot and ALCO

Abstract

In this paper, we explore a quantitative approach to querying inconsistent description logic knowledge bases. We consider weighted knowledge bases in which both axioms and assertions have (possibly infinite) weights, which are used to assign a cost to each interpretation based upon the axioms and assertions it violates. Two notions of certain and possible answer are defined by either considering interpretations whose cost does not exceed a given bound or restricting attention to optimal-cost interpretations. Our main contribution is a comprehensive analysis of the combined and data complexity of bounded cost satisfiability and certain and possible answer recognition, for description logics between ELbot and ALCO.