Logical foundations of information disclosure in ontology-based data integration

Benedikt, Michael; Grau, Bernardo Cuenca; Kostylev, Egor V.

doi:10.1016/j.artint.2018.06.002

Cited by 43 publications

(53 citation statements)

References 68 publications

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“…We point out that a PTIME upper bound for possible BCQs with mixed-world semantics has been shown in [Benedikt et al, 2016;Benedikt et al, 2018] for a more restricted notion of linear rule (and without PTIME-hardness and QPTIME results). The key difference with [Benedikt et al, 2018] and other works on mixed-world reasoning [Lutz et al, 2013;Lutz et al, 2015;Ahmetaj et al, 2016;Ngo et al, 2016] is that we adopt active-domain semantics, whereas these other works use classical semantics under which new values can appear in the open predicates. This has a very significant impact on the decidability and complexity of reasoning.…”

Section: Discussionmentioning

confidence: 80%

“…This has a very significant impact on the decidability and complexity of reasoning. For example, certainty of BCQs is decidable in our setting even for arbitrary existential rules, while it is undecidable under classical semantics; for frontier-guarded rules, certainty of BCQs was shown to be EXPTIME-complete in data complexity [Benedikt et al, 2016], while it is coNP-complete in data complexity for our setting. A notable similarity is that our PTIME membership results employ a greatest fixpoint construction, which is in the same spirit as techniques used in [Benedikt et al, 2018;Benedikt et al, 2016].…”

Section: Discussionmentioning

confidence: 85%

“…For example, certainty of BCQs is decidable in our setting even for arbitrary existential rules, while it is undecidable under classical semantics; for frontier-guarded rules, certainty of BCQs was shown to be EXPTIME-complete in data complexity [Benedikt et al, 2016], while it is coNP-complete in data complexity for our setting. A notable similarity is that our PTIME membership results employ a greatest fixpoint construction, which is in the same spirit as techniques used in [Benedikt et al, 2018;Benedikt et al, 2016]. Other non-trivial data tractability results have been obtained for fact certainty in the presence of linear disjunctive Datalog rules [Kaminski et al, 2016], and for exact views given as LAV source-to-target rules [Benedikt et al, 2018].…”

Section: Discussionmentioning

confidence: 85%

“…This motivates the consideration of mixed-world semantics, where the set of predicates is partitioned into closed and open predicates, and models are required to coincide with the instance on the closed predicates. Mixed-world OMQA was first explored for DL ontologies [Lutz et al, 2013;Lutz et al, 2015;Ahmetaj et al, 2016;Ngo et al, 2016] and has only recently been studied for existential rules [Benedikt et al, 2016]. Further variants of traditional OMQA semantics can be obtained by placing additional restrictions on the models.…”

Section: Introductionmentioning

confidence: 99%

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Mixed-World Reasoning with Existential Rules under Active-Domain Semantics

Bourhis

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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In this paper, we study reasoning with existential rules in a setting where some of the predicates may be closed (i.e., their content is fully specified by the data instance) and the remaining open predicates are interpreted under active-domain semantics. We show, unsurprisingly, that the main reasoning tasks (satisfiability and certainty / possibility of Boolean queries) are all intractable in data complexity in the general case. However, several positive (PTIME data) results are obtained for the linear fragment, and interestingly, these tractability results hold also for various extensions, e.g., with negated closed atoms and disjunctive rule heads. This motivates us to take a closer look at the linear fragment, exploring its expressivity and defining a fixpoint extension to approximate non-linear rules.

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Section: Discussionmentioning

confidence: 80%

Section: Discussionmentioning

confidence: 85%

Section: Discussionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

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Mixed-World Reasoning with Existential Rules under Active-Domain Semantics

Bourhis

2019

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence

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“…The question of whether a database with complete and incomplete predicates has complete information to answer a query has received significant attention [23,18]; these works focus on the complexity for variations of the problem when inclusion dependencies are given as database constraints. When reasoning about privacy, some or all tuples in selected database relations may be hidden for privacy reasons, and thus from the users' viewpoint such relations are incomplete [8,9]. This work, quite related to ours, focuses on visible and invisible tables.…”

Section: Related Workmentioning

confidence: 99%

Polynomial rewritings from expressive Description Logics with closed predicates to variants of Datalog

Ahmetaj

Ortiz

Šimkus

2020

Artificial Intelligence

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In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed-and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory that are to be interpreted under the closed-world assumption, while the rest are interpreted with the open-world view. In this way we can retrieve more precise answers to queries by leveraging the partial completeness of the data.The central goal of this paper is to understand the relative expressiveness of ontology-mediated query languages in which the ontology part is written in the expressive Description Logic (DL) ALCHOI and includes a set of closed predicates. We consider a restricted class of conjunctive queries. Our main result is to show that every query in this non-monotonic query language can be translated in polynomial time into DATALOG with negation as failure under the stable model semantics. To overcome the challenge that DATALOG has no direct means to express the existential quantification present in ALCHOI, we define a two-player game that characterizes the satisfaction of the ontology, and design a DATALOG query that can decide the existence of a winning strategy for the game. If there are no closed predicates-in the case of querying an ALCHOI knowledge base-our translation yields a positive disjunctive DATALOG program of polynomial size. To the best of our knowledge, unlike previous translations for related fragments with expressive (non-Horn) DLs, these are the first polynomial time translations.

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