All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs

Bednarczyk, Bartosz; Ferens, Robert; Ostropolski-Nalewaja, Piotr

doi:10.24963/ijcai.2020/238

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…A standard technique for checking universal termination of a chase is based on reducing the problem to checking termination for a single critical dataset (Marnette, 2009;Calautti et al, 2015;Calautti & Pieris, 2021;Bednarczyk et al, 2020). Depending on the type of chase, this technique may require specific modifications (Gogacz et al, 2020;Karimi et al, 2021).…”

Section: Related Problems and Techniquesmentioning

confidence: 99%

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Wałęga

Zawidzki²,

Grau³

2023

jair

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DatalogMTL is an extension of Datalog with metric temporal operators that has recently found applications in stream reasoning and temporal ontology-based data access. In contrast to plain Datalog, where materialisation (a.k.a. forward chaining) naturally terminates in finitely many steps, reaching a fixpoint in DatalogMTL may require infinitely many rounds of rule applications. As a result, existing reasoning systems resort to other approaches, such as constructing large Büchi automata, whose implementations turn out to be highly inefficient in practice. In this paper, we propose and study finitely materialisable DatalogMTL programs, for which forward chaining reasoning is guaranteed to terminate. We consider a data-dependent notion of finite materialisability of a program, where termination is guaranteed for a given dataset, as well as a data-independent notion, where termination is guaranteed regardless of the dataset. We show that, for bounded programs (a natural DatalogMTL fragment for which reasoning is as hard as in the full language), checking data-dependent finite materialisability is ExpSpace-complete in combined complexity and PSpace-complete in data complexity; furthermore, we propose a practical materialisation-based decision procedure that works in doubly exponential time. We show that checking data-independent finite materialisability for bounded progams is computationally easier, namely ExpTime-complete; moreover, we propose sufficient conditions for data-indenpendent finite materialisability that can be efficiently checked. We provide also the complexity landscape of fact entailment for different classes of finitely materialisable programs; surprisingly, we could identify a large class of finitely materialisable programs, called MTL-acyclic programs, for which fact entailment has exactly the same data and combined complexity as in plain Datalog, which makes this fragment especially well suited for big-scale applications.

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Section: Related Problems and Techniquesmentioning

confidence: 99%

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Wałęga

Zawidzki²,

Grau³

2023

jair

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“…Note that the undecidability of ∀∀ ( ) has been originally shown in [15] for schemas with binary and ternary predicates. The undecidability for schemas with binary predicates has been recently shown in [4] by adapting the proof of [15]. On the other hand, when it comes to the class of linear TGDs, we know that the above problem is decidable:…”

Section: Chase Termination Problemmentioning

confidence: 99%

All-Instances Restricted Chase Termination for Linear TGDs

2020

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The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances chase termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input database? In view of the fact that this problem is, in general, undecidable, it is natural to ask whether well-behaved classes of TGDs, introduced in different contexts, ensure decidability. It has been recently shown that the problem is decidable for the restricted (a.k.a. standard) version of the chase, and linear TGDs, a prominent class of TGDs that has been introduced in the context of ontological query answering, under the assumption that only one atom appears in TGD-heads. We provide an alternative proof for this result based on Monadic Second-Order Logic, which we believe is simpler that the ones obtained from the literature.

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All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs

Cited by 2 publications

References 12 publications

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Finite Materialisability of Datalog Programs with Metric Temporal Operators

All-Instances Restricted Chase Termination for Linear TGDs

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