Queries With Exact Truth Values in Paraconsistent Description Logics

TL;DR

This paper introduces a novel paraconsistent semantics for querying inconsistent description logic knowledge bases using four truth values, enabling differentiation of contradictory evidence and maintaining tractable data complexity for Horn DLs.

Contribution

It proposes a new approach allowing truth value operators in queries, extending prior work, and provides complexity analysis and comparison with repair-based semantics.

Findings

Queries with truth operators can distinguish contradictory evidence.

Tractable data complexity is preserved for Horn DLs.

The approach is incomparable with repair-based semantics.

Abstract

We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both ($\mathbf{B}$), and neither ($\mathbf{N}$). In contrast to prior studies on paraconsistent DLs, we allow truth value operators in the query language, which can be used to differentiate between answers having contradictory evidence and those having only positive evidence. We present a reduction to classical DL query answering that allows us to pinpoint the precise combined and data complexity of answering queries with values in paraconsistent $\mathcal{ALCHI}$ and its sublogics. Notably, we show that tractable data complexity is retained for Horn DLs. We present a comparison with repair-based inconsistency-tolerant semantics, showing that the two approaches are incomparable.