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SAT Encoding of Unification in \(\mathcal{ELH}_{{R}^+}\) w.r.t. Cycle-Restricted Ontologies

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7364)

Abstract

Unification in Description Logics has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the Description Logic \(\mathcal{EL}\), which is used to define several large biomedical ontologies, unification is NP-complete. An NP unification algorithm for \(\mathcal{EL}\) based on a translation into propositional satisfiability (SAT) has recently been presented. In this paper, we extend this SAT encoding in two directions: on the one hand, we add general concept inclusion axioms, and on the other hand, we add role hierarchies (\(\mathcal{H}\)) and transitive roles (R  + ). For the translation to be complete, however, the ontology needs to satisfy a certain cycle restriction. The SAT translation depends on a new rewriting-based characterization of subsumption w.r.t. \(\mathcal{ELH}_{{R}^+}\)-ontologies.

Supported by DFG under grant BA 1122/14-1.

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Baader, F., Borgwardt, S., Morawska, B. (2012). SAT Encoding of Unification in \(\mathcal{ELH}_{{R}^+}\) w.r.t. Cycle-Restricted Ontologies. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-31365-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31364-6

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