Model-theoretic Characterizations of Existential Rule Languages

Zhang, Heng; Zhang, Yan; Jiang, Guifei

doi:10.24963/ijcai.2020/269

Cited by 3 publications

(15 citation statements)

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“…Finally, we investigate the decision problems Rewrite(L, L ′ ), where L is the class of frontier-guarded tgds and L ′ is the class of guarded tgds, or L is the class of guarded tgds and L ′ is the class of linear tgds. In both these cases, we obtain complexity results that significantly sharpen the results established in [17].…”

Section: Summary Of Resultssupporting

confidence: 70%

“…More precisely, we can devise a finite set of guarded (respectively, frontierguarded) tgds that cannot be equivalently rewritten as a finite set of linear (respectively, guarded) tgds. Actually, those separations were folklore, and made explicit in the recent work [17]. The value of our analysis is that it provides further insights, using the linear and guarded locality properties, on why those separations hold.…”

Section: Relative Expressiveness and Rewritabilitymentioning

confidence: 64%

“…From Guarded to Linear. The problem Rewrite(GTGD, LTGD) has been already considered in the recent work [17]. It was shown to be PSpace-hard, but no decision procedure was provided.…”

Section: Rewritabilitymentioning

confidence: 99%

“…They also characterized when a first-order sentence is equivalent to a finite set of axioms in a certain description logic. Quite recently, Zhang et al [17] obtained model-theoretic characterizations of existential rule languages in the preservation approach. In particular, they characterized when a finite set of tgds is equivalent to (i) a finite set of frontier-guarded tgds; (ii) a finite set of guarded tgds; and (iii) a finite set of linear tgds.…”

Section: Introductionmentioning

confidence: 99%

“…The preservation approach between two logical formalisms L and L ′ gives rise to a natural decision problem, which we will denote by Rewrite(L, L ′ ): given a finite set of Σ of L-formulas, is there a finite set Σ ′ of L ′ -formulas such that Σ is equivalent to Σ ′ ? The papers [12] and [17] contain a number of complexity results about the decision problem Rewrite(L, L ′ ) for various logical formalisms L and L ′ .…”

Section: Introductionmentioning

confidence: 99%

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Model-theoretic Characterizations of Rule-based Ontologies

Console

Kolaitis

Pieris

2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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An ontology specifies an abstract model of a domain of interest via a formal language that is typically based on logic. Although description logics are popular formalisms for modeling ontologies, tuplegenerating dependencies (tgds), originally introduced as a unifying framework for database integrity constraints, and later on used in data exchange and integration, are also well suited for modeling ontologies that are intended for data-intensive tasks. The reason is that, unlike description logics, tgds can easily handle higherarity relations that naturally occur in relational databases. In recent years, there has been an extensive study of tgd-ontologies and of their applications to several different data-intensive tasks. However, the fundamental question of whether the expressive power of tgd-ontologies can be characterized in terms of model-theoretic properties remains largely unexplored. We establish several characterizations of tgd-ontologies, including characterizations of ontologies specified by such central classes of tgds as full, linear, guarded, and frontier-guarded tgds. Our characterizations use the well-known notions of critical instance and direct product, as well as a novel locality property for tgd-ontologies. We further use this locality property to decide whether an ontology expressed by frontier-guarded (respectively, guarded) tgds can be expressed by tgds in the weaker class of guarded (respectively, linear) tgds, and effectively construct such an equivalent ontology if one exists.

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Section: Summary Of Resultssupporting

confidence: 70%

Section: Relative Expressiveness and Rewritabilitymentioning

confidence: 64%

“…From Guarded to Linear. The problem Rewrite(GTGD, LTGD) has been already considered in the recent work [17]. It was shown to be PSpace-hard, but no decision procedure was provided.…”

Section: Rewritabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Model-theoretic Characterizations of Rule-based Ontologies

Console

Kolaitis

Pieris

2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Overharvesting in human patch foraging reflects rational structure learning and adaptive planning

Harhen

Bornstein

2023

Proc. Natl. Acad. Sci. U.S.A.

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Patch foraging presents a sequential decision-making problem widely studied across organisms—stay with a current option or leave it in search of a better alternative? Behavioral ecology has identified an optimal strategy for these decisions, but, across species, foragers systematically deviate from it, staying too long with an option or “overharvesting” relative to this optimum. Despite the ubiquity of this behavior, the mechanism underlying it remains unclear and an object of extensive investigation. Here, we address this gap by approaching foraging as both a decision-making and learning problem. Specifically, we propose a model in which foragers 1) rationally infer the structure of their environment and 2) use their uncertainty over the inferred structure representation to adaptively discount future rewards. We find that overharvesting can emerge from this rational statistical inference and uncertainty adaptation process. In a patch-leaving task, we show that human participants adapt their foraging to the richness and dynamics of the environment in ways consistent with our model. These findings suggest that definitions of optimal foraging could be extended by considering how foragers reduce and adapt to uncertainty over representations of their environment.

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Towards Universal Languages for Tractable Ontology Mediated Query Answering

Zhang

You

et al. 2020

AAAI

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An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

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Model-theoretic Characterizations of Existential Rule Languages

Cited by 3 publications

References 0 publications

Model-theoretic Characterizations of Rule-based Ontologies

Model-theoretic Characterizations of Rule-based Ontologies

Overharvesting in human patch foraging reflects rational structure learning and adaptive planning

Towards Universal Languages for Tractable Ontology Mediated Query Answering

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