A finite basis theorem for the description logic ${\cal ALC}$

13 Jan 2017  ·  Aiguier Marc, Atif Jamal, Bloch Isabelle, Hudelot Céline ·

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). read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Logic in Computer Science

Datasets


  Add Datasets introduced or used in this paper