Model-theoretic inseparability and modularity of description logic ontologies

Konev, Boris; Lutz, Carsten; Walther, Dirk; Wolter, Frank

doi:10.1016/j.artint.2013.07.004

Cited by 61 publications

(61 citation statements)

References 33 publications

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“…⊓ ⊔ Using the bounded model property established in Lemma 3, one can prove a coNExp NP upper bound for model inseparability. A matching lower bound and several extensions of this result are proved in [56].…”

Section: Undecidability Of Model Inseparabilitymentioning

confidence: 87%

See 1 more Smart Citation

Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering

Pan¹,

Calvanese²,

Eiter³

et al. 2017

Lecture Notes in Computer Science

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The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization, forgetting, and knowledge exchange. What 'safe replacement' means depends on the intended application of the ontology. If, for example, it is used to query data, then the answers to any relevant ontology-mediated query should be the same over any relevant data set; if, in contrast, the ontology is used for conceptual reasoning, then the entailed subsumptions between concept expressions should coincide. This gives rise to different notions of ontology inseparability such as query inseparability and concept inseparability, which generalize corresponding notions of conservative extensions. We survey results on various notions of inseparability in the context of description logic ontologies, discussing their applications, useful model-theoretic characterizations, algorithms for determining whether two ontologies are inseparable (and, sometimes, for computing the difference between them if they are not), and the computational complexity of this problem.ALC obtained by disallowing the constructors ⊥, ¬, ⊔ and ∀ is known as EL. Thus, EL concepts are constructed using ⊤, ⊓ and ∃ only [6]. We also consider extensions of EL with the constructors in Table 2. For example, ELI u denotes the extension of EL with inverse roles and the universal role. The fragments of ALCI and ALCHI, in which CIs are of the form

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Section: Undecidability Of Model Inseparabilitymentioning

confidence: 87%

“…The lower bound is proved in [56] by a reduction of satisfiability in circumscribed ALC KBs, which is known to be coNExp NP -hard. ⊓ ⊔…”

Section: Undecidability Of Model Inseparabilitymentioning

confidence: 99%

Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering

Pan¹,

Calvanese²,

Eiter³

et al. 2017

Lecture Notes in Computer Science

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show abstract

“…This means the method is not complete, but since no complete method can exist for forgetting, as considered in this paper with the target language being ALCOI, this is to be expected. Concept forgetting is already not always computable for the description logic EL [10]. We also note that when concept symbols cannot be eliminated by our method this does not necessarily mean that they are ineliminable.…”

Section: The Dsqel Forgetting Methodsmentioning

confidence: 99%

Concept Forgetting in $$\mathcal {ALCOI}$$-Ontologies Using an Ackermann Approach

Zhao

Schmidt

2015

The Semantic Web - ISWC 2015

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Abstract. We present a method for forgetting concept symbols in ontologies specified in the description logic ALCOI. The method is an adaptation and improvement of a second-order quantifier elimination method developed for modal logics and used for computing correspondence properties for modal axioms. It follows an approach exploiting a result of Ackermann adapted to description logics. An important feature inherited from the modal approach is that the inference rules are guided by an ordering compatible with the elimination order of the concept symbols. This provides more control over the inference process and reduces non-determinism, resulting in a smaller search space. The method is extended with a new case splitting inference rule, and several simplification rules. Compared to related forgetting and uniform interpolation methods for description logics, the method can handle inverse roles, nominals and ABoxes. Compared to the modal approach on which it is based, it is more efficient in time and improves the success rates. The method has been implemented in Java using the OWL API. Experimental results show that the order in which the concept symbols are eliminated significantly affects the success rate and efficiency.

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“…This notion has been studied for expressive DLs [51,47,52] and for Horn variants of DLs [53,54,55,30]. Two major forms of inseparability have been considered in the literature.…”

Section: Related Workmentioning

confidence: 99%

“…On one hand, this occurs when an ontology was updated and the update needs to be verified. On the other hand, modularization (or module extraction) aims at splitting a given ontology into smaller sub-ontologies, each of which can be used autonomously, when only a subset of the ontology signature is of interest [10,12,46,47]. Such sub-ontologies are called modules, and since they are typically of a small size (compared to the entire ontology, which can be very large), it is easier to understand them and perform reasoning with them.…”

Section: Related Workmentioning

confidence: 99%

Knowledge base exchange: The case of OWL 2 QL

Arenas

Botoeva

Calvanese

et al. 2016

Artificial Intelligence

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In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWL 2 QL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-Lite R . We develop novel gameand automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTime.

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Model-theoretic inseparability and modularity of description logic ontologies

Cited by 61 publications

References 33 publications

Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering

Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering

Concept Forgetting in $$\mathcal {ALCOI}$$-Ontologies Using an Ackermann Approach

Knowledge base exchange: The case of OWL 2 QL

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