Knowledge base exchange: The case of OWL 2 QL

Arenas, Marcelo; Botoeva, Elena; Calvanese, Diego; Ryzhikov, Vladislav

doi:10.1016/j.artint.2016.05.002

Cited by 9 publications

(7 citation statements)

References 52 publications

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“…(1) We observe that many inseparability relations considered above (in particular, concept inseparability) fail to satisfy natural robustness conditions such as robustness under replacement, and discuss how to overcome this. (2) Since inseparability tends to be of high computational complexity or even undecidable, it is interesting to develop approximation algorithms; we present a brief overview of the state of the art. (3) One is often not only interested in deciding inseparability, but also in computing useful members of an equivalence class of inseparable ontologies such as uniform interpolants and the result of forgetting irrelevant symbols from an ontology.…”

Section: Discussionmentioning

confidence: 99%

“…Forgetting under model inseparability has been studied extensively in logic [34] and more recently for DLs [107]. Note that the computation of universal CQ solutions in knowledge exchange [2] is identical to forgetting the signature of the original KB under Σ-CQ-inseparability.…”

Section: Discussionmentioning

confidence: 99%

“…This application is a natural extension of data exchange [29], where the task is to transform a data instance D 1 structured under a source schema Σ 1 into a data instance D 2 structured under a target schema Σ 2 given a mapping M 12 relating Σ 1 and Σ 2 . In knowledge base exchange [2], we are interested in translating a KB K 1 in a source signature Σ 1 to a KB K 2 in a target signature Σ 2 according to a mapping given by a TBox T 12 that consists of CIs and RIs in Σ 1 ∪ Σ 2 defining concept and role names in Σ 2 in terms of concepts and roles in Σ 1 . A good solution to this problem can be viewed as a KB K 2 that it is inseparable from K 1 ∪T 12 with respect to a suitable Σ 2 -inseparability relation.…”

Section: Inseparabilitymentioning

confidence: 99%

See 2 more Smart Citations

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: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Inseparabilitymentioning

confidence: 99%

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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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“…This problem has originally been studied for traditional relational databases where a decade of intensive research brought up a number of foundational and system oriented work [2,5,7,21,26]. More recently research in data exchange changed its focus in various directions that include non-relational [4] and temporal data [13], knowledge bases [3], mapping discovery [27,28], and probabilistic settings [19,25].…”

Section: Introductionmentioning

confidence: 99%

On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds

Forssell,

Kharlamov,

Thorstensen

2020

Preprint

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Data exchange heavily relies on the notion of incomplete database instances. Several semantics for such instances have been proposed and include open (OWA), closed (CWA), and open-closed (OCWA) world. For all these semantics important questions are: whether one incomplete instance semantically implies another; when two are semantically equivalent; and whether a smaller or smallest semantically equivalent instance exists. For OWA and CWA these questions are fully answered. For several variants of OCWA, however, they remain open. In this work we adress these questions for Closed Powerset semantics and the OCWA semantics of [24]. We define a new OCWA semantics, called OCWA*, in terms of homomorphic covers that subsumes both semantics, and characterize semantic implication and equivalence in terms of such covers. This characterization yields a guess-and-check algorithm to decide equivalence, and shows that the problem is NP-complete. For the minimization problem we show that for several common notions of minimality there is in general no unique minimal equivalent instance for Closed Powerset semantics, and consequently not for the more expressive OCWA* either. However, for Closed Powerset semantics we show that one can find, for any incomplete database, a unique finite set of its subinstances which are subinstances (up to renaming of nulls) of all instances semantically equivalent to the original incomplete one. We study properties of this set, and extend the analysis to OCWA*.

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“…This is the case for many real-world ontologies, which not only provide a conceptual model of the domain of interest, but also introduce the individuals relevant for the domain and their properties. In addition to versioning, modularisation, revision, update, and forgetting, applications of Σ-KB entailment and Σ-KB inseparability also include knowledge exchange [32,33,34], where a user wants to transform a KB K 1 given in a signature Σ 1 to a KB K 2 in a new signature Σ 2 connected to Σ 1 using a mapping M, also known as an ontology alignment or ontology matching [35]. The condition that the target KB K 2 is a sound and complete representation of K 1 under M with respect to the answers to a class Q of relevant queries can then be formulated as the condition that K 1 ∪ M and K 2 are Σ 2 -Q inseparable [34].…”

Section: Introductionmentioning

confidence: 99%

Query inseparability for ALC ontologies

Botoeva

Lutz

Ryzhikov

et al. 2019

Artificial Intelligence

Self Cite

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We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give modeltheoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop model-theoretic criteria for HornALC TBoxes and show using tree automata that, in contrast, inseparability becomes decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs. module is extracted from an ontology. In ontology update or revision, the difference between the answers to queries over the updated or revised ontology and the original one should be minimised when constructing update or revision operators. Similarly, in forgetting, it is the answers to queries which should be preserved under appropriate forgetting operators. Thus, in the context of query answering, the fundamental relationship between ontologies is not whether they are logically equivalent (have the same models), but whether they give the same answers to any relevant query. To illustrate, consider the following simple TBox T = {Book ∃author.¬Book} saying that every book has an author who is not a book. Clearly, T is not logically equivalent to the TBoxwhich only states that every book has an author. However, if one takes as the query language the popular classes of conjunctive queries (CQs) or unions of CQs (UCQs), then no matter what the data is, every query will have the same answers independently of whether one uses T or T . Intuitively, the reason is that the 'positive' information given by T coincides with the 'positive' information given by T . If the main purpose of the ontology is answering UCQs, it is thus more important to know that T can be safely replaced by T without affecting the answers to UCQs than to establish that T and T are not logically equivalent.In most ontology engineering applications for ontology-based data access, the relevant class Q of queries can be further restricted to those given in a finite signature of relevant concept and role names. For example, to establish that a subset M of an ontology O is a module of O, one should not require that M and O give the same answers to all queries in Q, but only to those that are in the signature of M. Similarly, in the versioning ...

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Knowledge base exchange: The case of OWL 2 QL

Cited by 9 publications

References 52 publications

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

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

On Equivalence and Cores for Incomplete Databases in Open and Closed Worlds

Query inseparability for ALC ontologies

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