Rigid E-unification: NP-completeness and applications to equational matings
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
The undecidability of simultaneous rigid E-unification
Theoretical Computer Science
Unification of concept terms in description logics
Journal of Symbolic Computation
Replacing SEP-Triplets in SNOMED CT Using Tractable Description Logic Operators
AIME '07 Proceedings of the 11th conference on Artificial Intelligence in Medicine
Unification in the Description Logic $\mathcal{EL}$
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
SAT encoding of unification in EL
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Representing transitive propagation in OWL
ER'06 Proceedings of the 25th international conference on Conceptual Modeling
A goal-oriented algorithm for unification in ELHR+ w.r.t. cycle-restricted ontologies
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
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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.