Cost-Based Semantics for Querying Inconsistent Weighted Knowledge Bases
Meghyn Bienvenu, Camille Bourgaux, Robin Jean
TL;DR
This work introduces a cost-based framework for querying inconsistent description logic knowledge bases by assigning infinite weights to hard axioms and finite weights to soft axioms, then evaluating answers with respect to either a cost bound $k$ or the optimal cost $ ext{optc}( ext{KB}_ ext{ω})$. It defines bounded-cost and optimal-cost notions for certain and possible answers, covers both $EL_ot$ and $ALCO$ with IQs and CQs, and derives a near-complete complexity landscape for combined and data complexity, including ExpTime and 2ExpTime results and corresponding lower bounds. The main methodological advances include the $k$-configuration technique and reductions to expressive DLs ($ ext{ALCOQ}^u$) to obtain upper bounds, together with reductions from classical DL and database problems to establish hardness. The paper situates its framework among related work on soft constraints, repairs, and circumscription, and highlights future work toward broader DL constructs and practical algorithms for implementation and scalability.
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.