Finitely Materialisable Datalog Programs with Metric Temporal Operators

Wałęga, Przemysław Andrzej; Zawidzki, Michał

doi:10.24963/kr.2021/59

Cited by 7 publications

(8 citation statements)

References 20 publications

(23 reference statements)

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“…PSpace-complete for data complexity P-complete for data complexity This paper constitutes a significant extension of our previous conference publication (Wałęga et al, 2021b).…”

Section: Expspace-completementioning

confidence: 90%

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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“…PSpace-complete for data complexity P-complete for data complexity This paper constitutes a significant extension of our previous conference publication (Wałęga et al, 2021b).…”

Section: Expspace-completementioning

confidence: 90%

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Wałęga

Zawidzki²,

Grau³

2023

jair

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“…In this section, we formulate the naïve materialisation procedure implicit in our theoretical results in [21] and implemented in the MeTeoR reasoner [22].…”

Section: Naïve Materialisation In Datalogmtlmentioning

confidence: 99%

“…In our recent work [22], we proposed a materialisation-based procedure optimised for efficient application of DatalogMTL rules by means of suitable temporal indices, and where partial materialisations are succinctly represented as sets of temporal facts. We also identified a fragment of DatalogMTL [21] for which our materialisation-based procedure is guaranteed to terminate; this fragment imposes suitable restrictions which effectively disallow programs expressing 'recursion through time'. To ensure termination in the general case for consistency and fact entailment tasks, we proposed and implemented in the MeTeoR system [22] an algorithm combining materialisation with the construction of Büchi automata, so that the use of automata-based techniques is minimised in favour of materialisation; thus, the scalability of this approach in most practical cases is critically dependent on that of its materialisation component.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose a seminaïve materialisation-based procedure for DatalogMTL, which can be seamlessly applied in isolation to finitely materialisable fragments [21], or used in the general case in combination with automatabased techniques [22]. As in [22], our procedure iteratively performs materialisation steps which compute partial materialisations consisting of temporal facts; furthermore, each materialisation step performs a round of rule applications followed by a coalescing phase where temporal facts differing only in their (overlapping) intervals are merged together.…”

Section: Introductionmentioning

confidence: 99%

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Seminaive Materialisation in DatalogMTL

Wang¹,

Wałęga²,

Grau³

2022

Preprint

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DatalogMTL is an extension of Datalog with metric temporal operators that has found applications in temporal ontology-based data access and query answering, as well as in stream reasoning. Practical algorithms for DatalogMTL are reliant on materialisation-based reasoning, where temporal facts are derived in a forward chaining manner in successive rounds of rule applications. Current materialisation-based procedures are, however, based on a naïve evaluation strategy, where the main source of inefficiency stems from redundant computations. In this paper, we propose a materialisation-based procedure which, analogously to the classical seminaïve algorithm in Datalog, aims at minimising redundant computation by ensuring that each temporal rule instance is considered at most once during the execution of the algorithm. Our experiments show that our optimised seminaïve strategy for DatalogMTL is able to significantly reduce materialisation times.

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“…Reasoning in DatalogMTL is, however, of high complexity, namely ExpSpace-complete (Brandt et al 2018) and PSpace-complete with respect to data size , which makes reasoning in practice challenging. Thus, research has recently focused on establishing a suitable tradeoff between expressive power and complexity of reasoning, by identifying lower complexity fragments of DatalogMTL (Wał ęga et al 2020b;Wał ęga, Zawidzki, and Cuenca Grau 2021) as well as studying alternative semantics with more favourable computational behaviour (Wał ęga et al 2020a;Ryzhikov, Wał ęga, and Zakharyaschev 2019).…”

Section: Introductionmentioning

confidence: 99%

MeTeoR: Practical Reasoning in Datalog with Metric Temporal Operators

Wang

Wałęga

et al. 2022

AAAI

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DatalogMTL is an extension of Datalog with operators from metric temporal logic which has received significant attention in recent years. It is a highly expressive knowledge representation language that is well-suited for applications in temporal ontology-based query answering and stream processing. Reasoning in DatalogMTL is, however, of high computational complexity, making implementation challenging and hindering its adoption in applications. In this paper, we present a novel approach for practical reasoning in DatalogMTL which combines materialisation (a.k.a. forward chaining) with automata-based techniques. We have implemented this approach in a reasoner called MeTeoR and evaluated its performance using a temporal extension of the Lehigh University Benchmark and a benchmark based on real-world meteorological data. Our experiments show that MeTeoR is a scalable system which enables reasoning over complex temporal rules and datasets involving tens of millions of temporal facts.

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Finitely Materialisable Datalog Programs with Metric Temporal Operators

Cited by 7 publications

References 20 publications

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Seminaive Materialisation in DatalogMTL

MeTeoR: Practical Reasoning in Datalog with Metric Temporal Operators

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