Unification in commutative theories
Journal of Symbolic Computation
Terminological reasoning is inherently intractable (research note)
Artificial Intelligence
Automatic recognition of tractability in inference relations
Journal of the ACM (JACM)
Unification of concept terms in description logics
Journal of Symbolic Computation
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
The description logic handbook
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Unification in the Description Logic $\mathcal{EL}$
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Terminological cycles in a description logic with existential restrictions
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Non-standard inferences in description logics
Non-standard inferences in description logics
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In recent years, the description logic EL has received a significant interest. The description logic EL is a knowledge representation formalism used e.g in natural language processing, configuration of technical systems, databases and biomedical ontologies. Unification is used there as a tool to recognize equivalent concepts. It has been proven that unification in EL is NP-complete. This result was based on a locality property of certain EL unifiers. In fact, the large medical ontology SNOMED CT was built on a subset of EL++ formalism, however, without top-concept. It would be interesting to investigate decidability of unification in extensions of EL without using top-concept. In this paper, we look at decidability of unification in EL without top (EL-τ). We show that a similar locality holds for EL-τ, but decidability of EL-τ unification does not follow immediately from locality as it does in the case of unification in EL. However, by restricting further the locality property, we prove that EL-τ unification is decidable and construct an NExpTime decision procedure for the problem. Moreover, the procedure allows us to compute a specific set of solutions to the unification problem.