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- W2578753802 abstract "The main result of this paper is to prove the existence of a finite basis in the description logic ${cal ALC}$. We show that the set of General Concept Inclusions (GCIs) holding in a finite model has always a finite basis, i.e. these GCIs can be derived from finitely many of the GCIs. This result extends a previous result from Baader and Distel, which showed the existence of a finite basis for GCIs holding in a finite model but for the inexpressive description logics ${cal EL}$ and ${cal EL}_{gfp}$. We also provide an algorithm for computing this finite basis, and prove its correctness. As a byproduct, we extend our finite basis theorem to any finitely generated complete covariety (i.e. any class of models closed under morphism domain, coproduct and quotient, and generated from a finite set of finite models)." @default.
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- W2578753802 date "2015-02-26" @default.
- W2578753802 modified "2023-09-25" @default.
- W2578753802 title "A finite basis theorem for the description logic ${cal ALC}$" @default.
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