Unification in the Description Logic EL

The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.Comment: 31page

Importing from functional knowledge bases - A preview -

We review several proposals for reusing knowledge from existing ontologies by importing concepts and related axioms, which start from a set of "identifiers of interest". In order to compare these and other potential proposals, we offer a formal definition of the notion of "importing knowledge" based on Levesque's functional characterization of knowledge bases using a Tell/Ask interface. This denition is parameterized by a set A of Ask operators. In this preliminary work we consider ways in which this definition can be used to capture aspects of prior proposals, and therefore provide a framework for comparison between them

On the Relative Expressiveness of Description Logics and Predicate Logics

It is natural to view concept and role definitions in Description Logics as expressing monadic and dyadic predicates in Predicate Calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by formulas in ¨L³, the subset of First Order Predicate Calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results in the literature concerning languages with limited numbers of variables, we get as corollaries the existence of formulae of FOPC which cannot be expressed as descriptions. We also show that by omitting role composition, descriptions express exactly the formulae in ¨L², which is known to be decidable

On the Relationship between Description Logic and Predicate Logic Queries

Description Languages (DLs) are descendants of the kl-one [15] knowledge representation system, and form the basis of several object-centered knowledge base management systems developed in recent years, including ones in industrial use. Originally used for conceptual modeling (to define views), DLs are seeing increased use as query languages for retrieving information. This paper, aimed at a general audience that includes database researchers, considers the relationship between the expressive power of DLs and that of query languages based on Predicate Calculus. We show that all descriptions built using constructors currently considered in the literature can be expressed as formulae of the First Order Predicate Calculus with at most three variable symbols, though we have to allow numeric quantifiers and infinitary disjunction in order to handle a couple of special constructors. Conversely, we show that all first-order queries (formulae with one free variable) built up from unary and bin..