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

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 reas...

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Bibliographic Details
Authors: Juan Pablo Muñoz, Everardo Bárcenas, Iván Martínez, José Ramón Enrique Arrazola
Format: article
Status:Published version
Publication Date:2016
Country:México
Institution:Benemérita Universidad Autónoma de Puebla
Repository:Redalyc-BUAP
OAI Identifier:oai:redalyc.org:61544821007
Online Access:https://www.redalyc.org/articulo.oa?id=61544821007
Access Level:Open access
Keyword:Computación
proof theory
(Hyper)sequents
Description logics
automated reasoning
Description
Summary: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.