This paper proposes a connection method \`a la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL $\mathcal{ALCH}$ extended with two typicality operators: one on (complex) concepts and one on role names. The language is a variant of defeasible DLs, as broadly studied in the literature over the past decade, in which most of these can be embedded. We revisit the definition of the matrix representation of a knowledge base and establish the conditions for a given axiom to be provable. We show that the calculus terminates and is sound and complete w.r.t. a DL version of the preferential semantics widely adopted in non-monotonic reasoning.

翻译：本文提出了一种面向容错描述逻辑（DLs）家族的Bibel式连接方法。在语言层面，我们采用带有两个典型性算子的DL $\mathcal{ALCH}$扩展：一个作用于（复杂）概念，一个作用于角色名称。该语言是过去十年文献中广泛研究的可废止描述逻辑的一种变体，大多数此类逻辑均可嵌入其中。我们重新审视了知识库矩阵表示的定义，并建立了给定公理可证明的条件。我们证明该演算过程是可终止的，并且在非单调推理中广泛采用的偏好语义的描述逻辑版本下是可靠且完备的。