Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey

Botoeva, Elena; Konev, Boris; Lutz, Carsten; Ryzhikov, Vladislav; Wolter, Frank; Zakharyaschev, Michael

doi:10.1007/978-3-319-49493-7_2

Cited by 23 publications

(32 citation statements)

References 62 publications

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“…Nevertheless, there is still a notable gap in our understanding of this notion: query entailment between TBoxes is poorly understood in Horn DLs with inverse roles, which are considered a crucial feature in many applications. There is in fact a reason for this: as has already been observed by Botoeva et al (2016aBotoeva et al ( , 2016b, standard techniques for Horn DLs without inverse roles fail when inverse roles are added. More precisely, for Horn DLs without inverse roles query entailment can be characterized by the existence of homomorphisms between universal models (Lutz & Wolter, 2010;Botoeva et al, 2016a).…”

Section: Introductionmentioning

confidence: 91%

“…CQ entailment has been studied for various DLs (Kontchakov, Pulina, Sattler, Schneider, Selmer, Wolter, & Zakharyaschev, 2009;Lutz & Wolter, 2010;Konev et al, 2012;Botoeva, Lutz, Ryzhikov, Wolter, & Zakharyaschev, 2019), also in the KB version (Botoeva, Kontchakov, Ryzhikov, Wolter, & Zakharyaschev, 2016b;Botoeva et al, 2019), and also for OBDA specifications that involve mappings between data sources and the ABox (Bienvenu & Rosati, 2015), see also the survey by Botoeva, Konev, Lutz, Ryzhikov, Wolter, and Zakharyaschev (2016a). Nevertheless, there is still a notable gap in our understanding of this notion: query entailment between TBoxes is poorly understood in Horn DLs with inverse roles, which are considered a crucial feature in many applications.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting characterizations provide an important foundation for decision procedures, often based on tree automata emptiness (Botoeva et al, 2016a). In the presence of inverse roles, however, such characterizations are only correct if one resorts to bounded homomorphisms, that is, if one requires the existence of an n-bounded homomorphism, for any n (Botoeva et al, 2016a(Botoeva et al, , 2016b. The unbounded n in n-bounded homomorphisms corresponds to CQs of unbounded size that can be used for separating the two TBoxes.…”

Section: Introductionmentioning

confidence: 99%

“…It is more appropriate than the query-based notions in applications that require conceptual reasoning rather than querying data. It was historically even the first notion of conservative extension studied for DLs (Ghilardi, Lutz, & Wolter, 2006); we again refer to the survey (Botoeva et al, 2016a) for a more detailed discussion. We show that deductive entailment, deductive inseparability, and deductive conservative extensions are 2ExpTime-complete for all DLs between ELI and ELHIF ⊥ ; again, the runtime of our algorithm is single exponential in the size of T 1 and double exponential in the size of T 2 .…”

Section: Introductionmentioning

confidence: 99%

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Conservative Extensions in Horn Description Logics with Inverse Roles

Jung

Lutz

Martel

et al. 2020

jair

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We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conservative Extensions in Horn Description Logics with Inverse Roles

Jung

Lutz

Martel

et al. 2020

jair

Self Cite

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“…We therefore also consider the classes of rooted CQs (rCQs) and UCQs (rUCQs). So far, query entailment and inseparability have been studied for Horn DL KBs [37], EL TBoxes [38,15], DL-Lite TBoxes [39], and also for OBDA specifications, that is, DL-Lite TBoxes with mappings [40]; for a recent survey see [41]. No results are yet available for non-Horn DLs (neither in the KB nor in the TBox case) and for expressive Horn DLs in the TBox case.…”

Section: Introductionmentioning

confidence: 99%

Query inseparability for ALC ontologies

Botoeva

Lutz

Ryzhikov

et al. 2019

Artificial Intelligence

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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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Computing Minimal Projection Modules for $$\mathcal{ELH}^{r}$$ -Terminologies

Chen¹,

Ludwig²,

Ma³

et al. 2019

Logics in Artificial Intelligence

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For the development of large-scale representations of knowledge, the application of methodologies and design principles becomes relevant. The knowledge may be organized in ontologies in a modular and hierarchical fashion. An upper-level (reference) ontology typically provides specifications of requirements, functions, design or standards that are to be complied with by domain ontologies for a specific task on a lower level (task ontology) in the hierarchy. Verifying whether and how specifications have been implemented by a task ontology becomes a challenge when relevant axioms of the domain ontology need to be inspected. We consider specifications to be defined using entailments of certain queries over a given vocabulary. For selecting the relevant axioms from task ontologies, we propose a novel module notion called projection module that entails the queries that follow from a reference ontology. We develop algorithms for computing minimal projection modules of Description Logic terminologies for subsumption, instance and conjunctive queries.This work is partially funded by the ANR project GoAsQ (ANR-15-CE23-0022).

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Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey

Cited by 23 publications

References 62 publications

Conservative Extensions in Horn Description Logics with Inverse Roles

Conservative Extensions in Horn Description Logics with Inverse Roles

Query inseparability for ALC ontologies

Computing Minimal Projection Modules for $$\mathcal{ELH}^{r}$$ -Terminologies

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