The Space-Efficient Core of Vadalog

Berger, Gérald; Gottlob, Georg; Pieris, Andréas; Sallinger, Emanuel

doi:10.1145/3488720

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…This section fixes the basics that are needed to define dyadic decomposable sets, by providing a uniform notation for key existing notions: affected/invaded positions and attacked/protected/harmless/harmful/dangerous variables [4,6,18,19]. Basically, these notions serve to separate positions in which the chase can introduce only constants from those where nulls might appear.…”

Section: Preliminary Notionsmentioning

confidence: 99%

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Dyadic Existential Rules

GOTTLOB,

MANNA,

MARTE

2023

Theory and Practice of Logic Programming

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Existential rules form an expressive ${{\textsf{Datalog}}}$ -based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, only some of these classes fully encompass ${{\textsf{Datalog}}}$ and, often, this comes at the price of higher computational complexity. Moreover, expressive classes are typically unable to exploit tools developed for classes exhibiting lower expressiveness. To mitigate these shortcomings, this paper introduces a novel general syntactic condition that allows us to define, systematically and in a uniform way, from any decidable class $\mathcal{C}$ of existential rules, a new class called ${{\textsf{Dyadic-}\mathcal{C}}}$ enjoying the following properties: (i) it is decidable; (ii) it generalizes ${{\textsf{Datalog}}}$ ; (iii) it generalizes $\mathcal{C}$ ; (iv) it can effectively exploit any reasoner for query answering over $\mathcal{C}$ ; and (v) its computational complexity does not exceed the highest between the one of $\mathcal{C}$ and the one of ${{\textsf{Datalog}}}$ .

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Section: Preliminary Notionsmentioning

confidence: 99%

“…We start this section recalling the syntactic condition of the class Ward [10,19], useful for the comprehension of the new class Ward + that we will introduce below. We point out that we state the wardedness condition according to Definition 2; hence, the class Ward presented here is actually larger than the original one.…”

Section: Ward +mentioning

confidence: 99%

Dyadic Existential Rules

GOTTLOB,

MANNA,

MARTE

2023

Theory and Practice of Logic Programming

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“…Notice that in the presented results we focus on programs with finite Datalog ∃ chase which, as we have shown, allows us to construct finite chases in t-Datalog ∃ . However, there are prominent fragments of Datalog ∃ , such as (weakly) guarded [12] or warded [9] programs, where entailment is decidable even though the chase is generally not finite. Our truth-greedy chase technique does not provide us with an appropriate tool for reasoning in such cases.…”

Section: Adding Negation and Other Unary Operatorsmentioning

confidence: 99%

MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Lanzinger¹,

Sferrazza²,

Gottlob³

2022

Theory and Practice of Logic Programming

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Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and $\mathrm{MV-Datalog}^\pm$ as extensions of Datalog and $\mathrm{Datalog}^\pm$ , respectively, to the fuzzy semantics of infinite-valued Łukasiewicz logic $\mathbf{L}$ as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending $\mathrm{Datalog}^\pm$ .

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“…Notice that in the presented results we focus on programs with finite Datalog ∃ chase which, as we have shown, allows us to construct finite chases in t-Datalog ∃ . However, there are prominent fragments of Datalog ∃ , such as (weakly) guarded [13] or warded [9] programs, where entailment is decidable even though the chase is generally not finite. Our truth-greedy chase technique does not provide us with an appropriate tool for reasoning in such cases.…”

Section: Adding Negation and Other Unary Operatorsmentioning

confidence: 99%

Fuzzy Datalog∃ over Arbitrary t-Norms

Lanzinger,

Sferrazza,

Wałęga

et al.

EPiC Series in Computing

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One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model predictions, structured databases, crowd-sourced data, and many more. To allow for such reasoning, we generalise the standard rule-based language Datalog with existential rules (commonly referred to as tuple-generating dependencies) to the fuzzy setting, by allowing for arbitrary t-norms in the place of classical conjunctions in rule bodies. The resulting formalism allows us to perform reasoning about data associated with degrees of uncertainty while preserving computational complexity results and the applicability of reasoning techniques established for the standard Datalog setting. In particular, we provide fuzzy extensions of Datalog chases which produce fuzzy universal models and we exploit them to show that in important fragments of the language, reasoning has the same complexity as in the classical setting.

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The Space-Efficient Core of Vadalog

Cited by 4 publications

References 27 publications

Dyadic Existential Rules

Dyadic Existential Rules

MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Fuzzy Datalog∃ over Arbitrary t-Norms

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