Hybrid Unification in the Description Logic EL (original) (raw)

Computing Research Repository - CORR, 2010

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.

Unification in the Description Logic mathcalEL\mathcal{EL}mathcalEL without the Top Concept

Lecture Notes in Computer Science, 2011

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 recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive 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 in this paper that unification in EL without the top concept is PSpace-complete. example, the concept term ∃job. subsumes (i.e., is a superconcept of) the concept term ∃job.Boring since anyone that has a boring job at least has some job. Two concept terms are called equivalent if they subsume each other, i.e., if they are always interpreted as the same set of individuals.

Unification in the Description Logic EL \mathcal{EL} without the Top Concept

2000

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 \(\mathcal{EL}\) is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using \(\mathcal{EL}\) . On the other hand, unification in \(\mathcal{EL}\) has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, \(\mathcal{EL}\) 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 \(\mathcal{EL}\) makes the unification problem considerably harder. More precisely, we will show in this paper that unification in \(\mathcal{EL}\) without the top concept is PSpace-complete.

Unification in the Description Logic mathcalEL\mathcal{EL}mathcalEL

Lecture Notes in Computer Science, 2009

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, we show that EL-unification is NP-complete, and thus has the same complexity as EL-matching.

Unification in the Description Logic

2011

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, we show that EL-unification is NP-complete, and thus has the same complexity as EL-matching.

Anti-Unification of Concepts in Description Logic EL

2016

We study anti-unification for the description logic EL and introduce the notion of least general generalisation, which generalises simultaneously least common subsumer and concept matching. The idea of generalisation of two concepts is to detect maximal similarities between them, and to abstract over their differences uniformly. We demonstrate that a finite minimal complete set of generalisations for EL concepts always exists and establish complexity bounds for computing them. We present an anti-unification algorithm that computes generalisations with a fixed skeleton, study its properties and report on preliminary experimental evaluation.

Hybrid EL-Unification is NP-complete

2013

Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. However, the unification algorithms for EL developed until recently could not deal with ontologies containing general concept inclusions (GCIs). In a series of recent papers we have made some progress towards addressing this problem, but the ontologies the developed unification algorithms can deal with need to satisfy a certain cycle restriction. In the present paper, we follow a different approach. Instead of restricting the input ontologies, we generalize the notion of unifiers to so-called hybrid unifiers. Whereas classical unifiers can be viewed as acyclic TBoxes, hybrid unifiers are cyclic TBoxes, which are interpreted together with the ontology of the input using a hybrid semantics that combines fixpoint and descriptive semant...

Unification of Concept Terms in Description Logics: Revised Version

1998

Uni cation of concept terms is a new kind of inference problem for Description Logics, which extends the equivalence problem by allowing to substitute certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present rst decidability and complexity results for a small concept description language.

Unification of Concept Terms in Description Logics

Journal of Symbolic Computation, 2001

Extending Unification in EL towards General TBoxes

2012

Unification in Description Logics (DLs) has been proposed as an 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 recently been shown to be NP-complete, and thus of significantly lower complexity than unification in other DLs of similarly restricted expressive power. However, the unification algorithms for EL developed so far cannot deal with general concept inclusion axioms (GCIs). This paper makes a considerable step towards addressing this problem, but the GCIs our new unification algorithm can deal with still need to satisfy a certain cycle restriction.

Hybrid Unification in the Description Logic EL (original) (raw)

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