Abstract

MUNOZ, Juan Pablo; BARCENAS, Everardo; MARTINEZ, Iván  and  ARRAZOLA, José Ramón Enrique. (Hyper)sequent Calculi for the ALC(S4) Description Logics. Comp. y Sist. [online]. 2016, vol.20, n.1, pp.67-79. ISSN 2007-9737.  https://doi.org/10.13053/cys-20-1-2186.

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.

Keywords : Description logics; (Hyper)sequents; proof theory; automated reasoning.

        · text in English     · English ( pdf )