The Complexity of Circumscription in DLs

Bonatti, Piero A.; Lutz, Carsten; Wolter, Frank

doi:10.1613/jair.2763

Cited by 83 publications

(105 citation statements)

References 47 publications

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“…We argue in Section 4.2 that this case captures several relevant applications. We exhibit an interesting connection to DLs with circumscription [27,28] and use it to show coNExp NP -completeness for the inseparability of acyclic and general TBoxes formulated in ALC and ALCI. 2 (ii) The case where T 2 = ∅, which corresponds to deciding safety for a signature as discussed in the previous section, and which is still undecidable for acyclic ALC-TBoxes.…”

Section: Deciding Inseparability In Alc and Alcimentioning

confidence: 99%

“…Our main technical tool is a close correspondence between Σ-inseparability w.r.t. concept signatures and satisfiability of a certain kind of TBoxes with circumscription [28], which is interesting in its own right. We start with introducing TBoxes with circumscription.…”

Section: Concept Signaturesmentioning

confidence: 99%

“…Circ M,F (T ) if there is a model I of Circ M,F (T ) with C I = ∅. It is shown in [28] that satisfiability of concepts w.r.t. circumscribed TBoxes formulated in ALC or ALCI is NExp NP -complete.…”

Section: Concept Signaturesmentioning

confidence: 99%

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Model-theoretic inseparability and modularity of description logic ontologies

Konev

Lutz

Walther

et al. 2013

Artificial Intelligence

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The aim of this paper is to introduce and study model-theoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called modeltheoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ if they cannot be distinguished by the Σ-reducts of their models and thus can equivalently be replaced by one another in any application where only vocabulary items from Σ are relevant. We study in-depth the complexity of deciding inseparability for the description logics EL and ALC and their extensions with inverse roles. We then discuss notions of modules of a TBox based on model-theoretic inseparability and develop algorithms for extracting minimal modules from acyclic TBoxes. Finally, we provide an experimental evaluation of our module extraction algorithm based on the large-scale medical TBox Snomed ct.

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Section: Deciding Inseparability In Alc and Alcimentioning

confidence: 99%

Section: Concept Signaturesmentioning

confidence: 99%

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Model-theoretic inseparability and modularity of description logic ontologies

Konev

Lutz

Walther

et al. 2013

Artificial Intelligence

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“…Symbols declared after the minimisation can be varied. This is borrowed from circumscription [26,3]. Alternatively, the non-logical symbols to be minimised and to be varied can be explicitly declared: O minimize Σ 1 vars Σ 2 .…”

Section: Endmentioning

confidence: 99%

The Distributed Ontology, Modeling and Specification Language – DOL

Mossakowski¹,

Codescu²,

Neuhaus³

et al. 2015

Studies in Universal Logic

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Abstract. There is a diversity of ontology languages in use, among them OWL, RDF, OBO, Common Logic, and F-logic. Related languages such as UML class diagrams, entity-relationship diagrams and object role modelling provide bridges from ontology modelling to applications, e.g. in software engineering and databases. Another diversity appears at the level of ontology modularity and relations among ontologies. There is ontology matching and alignment, module extraction, interpolation, ontologies linked by bridges, interpretation and refinement, and combination of ontologies. The Distributed Ontology, Modelling and Specification Language (DOL) aims at providing a unified meta language for handling this diversity. In particular, DOL provides constructs for (1) "as-is" use of ontologies formulated in a specific ontology language, (2) ontologies formalised in heterogeneous logics, (3) modular ontologies, and (4) links between ontologies. This paper sketches the design of the DOL language. DOL will be submitted as a proposal within the OntoIOp (Ontology Integration and Interoperability) standardisation activity of the Object Management Group (OMG).

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“…We also know of some mature Circumscriptive [20] approaches that have been implemented [3,4]. However, the performance results of such implementations remain unpublished to the best of our knowledge.…”

Section: Related Workmentioning

confidence: 99%

Introducing Defeasibility into OWL Ontologies

Casini

Meyer

Moodley

et al. 2015

The Semantic Web - ISWC 2015

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Abstract. In recent years, various approaches have been developed for representing and reasoning with exceptions in OWL. The price one pays for such capabilities, in terms of practical performance, is an important factor that is yet to be quantified comprehensively. A major barrier is the lack of naturally occurring ontologies with defeasible features -the ideal candidates for evaluation. Such data is unavailable due to absence of tool support for representing defeasible features. In the past, defeasible reasoning implementations have favoured automated generation of defeasible ontologies. While this suffices as a preliminary approach, we posit that a method somewhere in between these two would yield more meaningful results. In this work, we describe a systematic approach to modify real-world OWL ontologies to include defeasible features, and we apply this to the Manchester OWL Repository to generate defeasible ontologies for evaluating our reasoner DIP (Defeasible-Inference Platform). The results of this evaluation are provided together with some insights into where the performance bottle-necks lie for this kind of reasoning. We found that reasoning was feasible on the whole, with surprisingly few bottle-necks in our evaluation.

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The Complexity of Circumscription in DLs

Cited by 83 publications

References 47 publications

Model-theoretic inseparability and modularity of description logic ontologies

Model-theoretic inseparability and modularity of description logic ontologies

The Distributed Ontology, Modeling and Specification Language – DOL

Introducing Defeasibility into OWL Ontologies

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