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

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.