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Extending unification in EL towards general TBoxes
 In Proc. KR’12. AAAI
, 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 de ..."
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Cited by 13 (13 self)
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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 NPcomplete, 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. 1
B.: A goaloriented algorithm for unification in ELHR+ w.r.t. cyclerestricted ontologies. LTCSReport 1205
, 2012
"... Abstract 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 NPcomplete. A goaloriented NP unification alg ..."
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Cited by 6 (6 self)
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Abstract 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 NPcomplete. A goaloriented NP unification algorithm for EL that uses nondeterministic rules to transform a given unification problem into solved form has recently been presented. In this paper, we extend this goaloriented algorithm in two directions: on the one hand, we add general concept inclusion axioms (GCIs), and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the algorithm to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction. 1
SAT encoding of unification in EL
 In Proc. LPAR’10, volume 6397 of LNCS
, 2010
"... Abstract. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in EL is NPcomplete, and thus of a complexity that is considerably lower than in other D ..."
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Abstract. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. In a recent paper, we have shown that unification in EL is NPcomplete, and thus of a complexity that is considerably lower than in other Description Logics of comparably restricted expressive power. In this paper, we introduce a new NPalgorithm for solving unification problems in EL, which is based on a reduction to satisfiability in propositional logic (SAT). The advantage of this new algorithm is, on the one hand, that it allows us to employ highly optimized stateoftheart SAT solvers when implementing an ELunification algorithm. On the other hand, this reduction provides us with a proof of the fact that ELunification is in NP that is much simpler than the one given in our previous paper on ELunification. 1
UEL: Unification Solver for EL
"... UEL is a system that computes unifiers for unification problems formulated in the description logic EL. EL is a description logic with restricted expressivity, but which is still expressive enough for the formal representation of biomedical ontologies, such as the large medical ontology SNOMED CT. ..."
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Cited by 5 (5 self)
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UEL is a system that computes unifiers for unification problems formulated in the description logic EL. EL is a description logic with restricted expressivity, but which is still expressive enough for the formal representation of biomedical ontologies, such as the large medical ontology SNOMED CT. We propose to use UEL as a tool to detect redundancies in such ontologies by computing unifiers of two formal concepts suspected of expressing the same concept of the application domain. UEL provides access to two different unification algorithms and can be used as a plugin of the popular ontology editor Protégé, or standalone.
A GoalOriented Algorithm for Unification in EL w.r.t. CycleRestricted TBoxes
 In Proceedings of the 25th International Workshop on Description Logics (DL’12), CEUR Workshop Proceedings
, 2012
"... Unification in DLs has been proposed in [7] (for the DL FL0, which offers the constructors conjunction (⊓), value restriction (∀r.C), and the top concept (⊤)) as a novel inference service that can, for instance, be used to detect redundancies in ontologies. For example, assume that one developer of ..."
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Cited by 4 (3 self)
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Unification in DLs has been proposed in [7] (for the DL FL0, which offers the constructors conjunction (⊓), value restriction (∀r.C), and the top concept (⊤)) as a novel inference service that can, for instance, be used to detect redundancies in ontologies. For example, assume that one developer of a medical ontology
B.: SAT encoding of unification in ELHR+ w.r.t. cyclerestricted ontologies
, 2012
"... Abstract. 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 EL, which is used to define several large biomedical ontologies, unification is NPcomplete. An NP unification algori ..."
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Cited by 4 (4 self)
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Abstract. 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 EL, which is used to define several large biomedical ontologies, unification is NPcomplete. An NP unification algorithm for 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 (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 rewritingbased characterization of subsumption w.r.t. ELHR+ontologies.
Computing Minimal ELunifiers is Hard
"... Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate un ..."
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Cited by 2 (2 self)
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Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NPcomplete problem. It is known that every solvable ELunification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) nonminimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for ELunification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative. Keywords:
ADMISSIBILITY IN FINITELY GENERATED QUASIVARIETIES ∗
, 2012
"... Vol. 9(2:09)2013, pp. 1–19 www.lmcsonline.org ..."
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Unification in the Description Logic EL without the Top Concept
"... Abstract. 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 ..."
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Cited by 1 (1 self)
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Abstract. 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 NPcomplete, 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 that unification in EL without the top concept is PSpacecomplete. 1