A connection method for a defeasible extension of 𝒜ℒ𝒞ℋ
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This paper proposes a connection method à la Bibel for an exception-tolerant family of description logics (DLs). As for the language, we assume the DL 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.
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