(Hyper)sequent Calculi for the ALC(S4) Description Logics

Juan Pablo Muñoz, Everardo Bárcenas, Iván Martínez, José Ramón Enrique Arrazola


Description logics (DL) form a well-known family of knowledge representation languages. One of its main applications is on the Semantic Web as a reasoning framework in the form of the Ontology Web Language (OWL). In this paper, we propose a cut-free tree hypersequent calculus for terminological reasoning in the Description Logic ALC. We show the calculus is sound and complete. Also, an implementation is provided together with a complexity analysis. In addition, we also describe a cut-free sequent calculus for the description logic ALC with reflexive and transitive roles. Soundness and completeness are proven, and a complexity analysis and an implementation are also provided.


Description logics, (Hyper)sequents, proof theory, automated reasoning.

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