Deciding Unifiability and Computing Local Unifiers in the Description Logic $\mathcal{E\!L}$ without Top Constructor

Franz Baader, Nguyen Thanh Binh, Stefan Borgwardt, Barbara Morawska
2016 Notre Dame Journal of Formal Logic  
Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive description logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has been shown to be NP-complete, and thus of considerably lower complexity than unification in other description logics of similarly restricted
more » ... sive power. However, EL allows the use of the top concept ( ), which represents the whole interpretation domain, whereas the large medical ontology SNOMED CT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSPACE-complete. In addition to the decision problem, we also consider the problem of actually computing EL − -unifiers. Introduction Description logics (DLs) [8] are a well-investigated family of logic-based knowledge representation formalisms. They can be used to represent the relevant concepts of an application domain using concept terms, which are built from concept names and role names using certain concept constructors. The DL EL offers the constructors conjunction ( ), existential restriction (∃r.C), and the top concept ( ). From a semantic point of view, concept names and concept terms represent sets of individuals, whereas roles represent binary relations between individuals. The top concept is interpreted as the set of all individuals. For example, using the concept names Male, Female, Person and the role names child, job, the concept of persons having a son, a daughter, and a job can be represented by the EL-concept term Person ∃child.Male ∃child.Female ∃job. .
doi:10.1215/00294527-3555507 fatcat:furoxuvajnhbtdgqhqbeakoo24