SAT Encoding of Unification in $\mathcal{ELH}_{{R}^+}$ w.r.t. Cycle-Restricted Ontologies

Baader, Franz; Borgwardt, Stefan; Morawska, Barbara

doi:10.1007/978-3-642-31365-3_5

Cited by 7 publications

(10 citation statements)

References 11 publications

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“…ELH R + -ontologies as unification in the equational theory SLmO of semilattices with monotone operators, using additional identities to express GCIs and role inclusions [6,15]. This unification-theoretic point of view sheds some light on our decision to restrict unification to the case of ground ontologies.…”

Section: Connection To E-unificationmentioning

confidence: 99%

“…We can show that this condition needs to be checked only for the cases where C is a concept name or . This allows us to decide in polynomial time whether an ELH R + -ontology is cycle-restricted [6].…”

Section: Cycle-restricted Ontologiesmentioning

confidence: 99%

“…We have developed two approaches for proving these characterizations: one based on term rewriting [6] and another one based on a sequent calculus for subsumption [3,5]. Previous algorithms for EL-unification w.r.t.…”

Section: Unification Algorithmsmentioning

confidence: 99%

“…the empty ontology were based on an even simpler characterization of subsumption that only had to take into account the structure of the compared concept descriptions [8,9,10]. Each of the following algorithms is based on one of those earlier algorithms and generalizes it using one of the characterizations from [5] and [6]. Before we can describe the algorithms, we need some additional definitions.…”

Section: Unification Algorithmsmentioning

confidence: 99%

“…In the following, we restrict both the unification problem Γ and the TBox T to contain only flat concept descriptions. This restriction is without loss of generality [6].…”

Section: Unification Algorithmsmentioning

confidence: 99%

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Recent Advances in Unification for the EL Family

Baader¹,

Borgwardt²,

Morawska³

EPiC Series in Computing

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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. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. Several algorithms that solve unification in EL have previously been presented. In this paper, we summarize recent extensions of these algorithms that can deal with general concept inclusion axioms (GCIs), role hierarchies (H), and transitive roles (R + ). For the algorithms to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction.

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Section: Connection To E-unificationmentioning

confidence: 99%

Section: Cycle-restricted Ontologiesmentioning

confidence: 99%

Section: Unification Algorithmsmentioning

confidence: 99%

Section: Unification Algorithmsmentioning

confidence: 99%

“…In the following, we restrict both the unification problem Γ and the TBox T to contain only flat concept descriptions. This restriction is without loss of generality [6].…”

Section: Unification Algorithmsmentioning

confidence: 99%

See 3 more Smart Citations

Recent Advances in Unification for the EL Family

Baader¹,

Borgwardt²,

Morawska³

EPiC Series in Computing

Self Cite

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Optimal Repairs in the Description Logic $$\mathcal{E}\mathcal{L}$$ Revisited

Baader,

Koopmann,

Kriegel

2023

Lecture Notes in Computer Science

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Unification in the Description Logic $$\mathcal {ELH}_{\mathcal {R}^+}$$ Without the Top Concept Modulo Cycle-Restricted Ontologies

Baader,

Fernández Gil

2024

Automated Reasoning

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Unification has been introduced in Description Logic (DL) as a means to detect redundancies in ontologies. In particular, it was shown that testing unifiability in the DL $$\mathcal{E}\mathcal{L}$$ E L is an NP-complete problem, and this result has been extended in several directions. Surprisingly, it turned out that the complexity increases to PSpace if one disallows the use of the top concept in concept descriptions. Motivated by features of the medical ontology SNOMED CT, we extend this result to a setting where the top concept is disallowed, but there is a background ontology consisting of restricted forms of concept and role inclusion axioms. We are able to show that the presence of such axioms does not increase the complexity of unification without top, i.e., testing for unifiability remains a PSpace-complete problem.

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SAT Encoding of Unification in $\mathcal{ELH}_{{R}^+}$ w.r.t. Cycle-Restricted Ontologies

Cited by 7 publications

References 11 publications

Recent Advances in Unification for the EL Family

Recent Advances in Unification for the EL Family

Optimal Repairs in the Description Logic $$\mathcal{E}\mathcal{L}$$ Revisited

Unification in the Description Logic $$\mathcal {ELH}_{\mathcal {R}^+}$$ Without the Top Concept Modulo Cycle-Restricted Ontologies

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