Data Complexity of Querying Description Logic Knowledge Bases under Cost-Based Semantics

TL;DR

This paper analyzes the data complexity of querying inconsistent weighted description logic knowledge bases under cost-based semantics, extending previous work to more expressive DLs and identifying cases where efficient computation is possible.

Contribution

It provides a detailed complexity analysis for cost-based semantics in expressive DLs, including sharp bounds and a surprising tractability result for certain DL-Lite fragments.

Findings

Sharpened lower bounds for data complexity of cost-based semantics.

Precise complexity characterization of optimal-cost certain answer semantics.

Identification of cases where query answering is in first-order rewritable and computationally efficient.

Abstract

In this paper, we study the data complexity of querying inconsistent weighted description logic (DL) knowledge bases under recently-introduced cost-based semantics. In a nutshell, the idea is to assign each interpretation a cost based upon the weights of the violated axioms and assertions, and certain and possible query answers are determined by considering all (resp. some) interpretations having optimal or bounded cost. Whereas the initial study of cost-based semantics focused on DLs between $\mathcal{EL}_\bot$ and $\mathcal{ALCO}$, we consider DLs that may contain inverse roles and role inclusions, thus covering prominent DL-Lite dialects. Our data complexity analysis goes significantly beyond existing results by sharpening several lower bounds and pinpointing the precise complexity of optimal-cost certain answer semantics (no non-trivial upper bound was known). Moreover, while all existing results show the intractability of cost-based semantics, our most challenging and surprising result establishes that if we consider $\text{DL-Lite}^\mathcal{H}_\mathsf{bool}$ ontologies and a fixed cost bound, certain answers for instance queries and possible answers for conjunctive queries can be computed using first-order rewriting and thus enjoy the lowest possible data complexity ($\mathsf{TC}_0$).