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.

翻译：我们提出了一种新颖的方法，用于查询经典不一致的描述逻辑知识库，该方法采用具有四个贝尔纳普真值的悖论容忍语义：精确真($\mathbf{T}$)、精确假($\mathbf{F}$)、两者($\mathbf{B}$)和皆非($\mathbf{N}$)。与先前关于悖论容忍描述逻辑的研究不同，我们在查询语言中允许使用真值运算符，这些运算符可用于区分具有矛盾证据的答案和仅具有正面证据的答案。我们提出了一种到经典描述逻辑查询应答的归约方法，这使得我们能够精确确定在悖论容忍$\mathcal{ALCHI}$及其子逻辑中回答具有真值的查询的精确组合复杂度和数据复杂度。值得注意的是，我们证明了对于Horn描述逻辑，可处理的数据复杂度得以保留。我们提出了与基于修复的不一致性容忍语义的比较，表明这两种方法是不可比较的。