Temporal Ontology-Mediated Queries and First-Order Rewritability: A Short Course

Ryzhikov, Vladislav; Wałęga, Przemysław Andrzej; Zakharyaschev, Michael

doi:10.1007/978-3-030-60067-9_5

Cited by 3 publications

(2 citation statements)

References 71 publications

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“…Operators from MTL have also been exploited in temporal extensions of description logics (DLs) (Gutiérrez-Basulto et al, 2016c;Baader et al, 2017;Thost, 2018;Artale & Franconi, 1998). Other temporal DLs rely on LTL operators or interval operators from the Halpern-Shoham logic, among others (Ozaki et al, 2018;Kovtunova, 2017;Artale & Franconi, 2000;Ryzhikov et al, 2020;Artale et al, , 2015aArtale et al, , 2015bGutiérrez-Basulto et al, 2016b).…”

Section: Languages For Temporal Reasoningmentioning

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: Languages For Temporal Reasoningmentioning

confidence: 99%

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Wałęga

Zawidzki²,

Grau³

2023

jair

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“…(1) work on OMQ answering over temporal data with discrete linear time and (2) work on temporal deductive databases. For detailed recent surveys of temporal OMQ answering in general we refer the reader to (Artale, Kontchakov, Kovtunova, Ryzhikov, Wolter, & Zakharyaschev, 2017;Ryzhikov, Walega, & Zakharyaschev, 2020).…”

Section: Related Workmentioning

confidence: 99%

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Artale¹,

Kontchakov²,

Kovtunova³

et al. 2021

Preprint

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Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z, <). Our main concern is firstorder rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<)-first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals-its extension FO(<, ≡) with the standard congruence predicates t ≡ 0 (mod n), for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FO(<, ≡)and FO(RPR)rewritability guarantee answering OMQs in uniform AC 0 and NC 1 , respectively.We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies.

show abstract

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Artale¹,

Kontchakov²,

Kovtunova³

et al. 2022

jair

View full text Add to dashboard Cite

Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z,<). Our main concern is first-order rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<) -- first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals---its extension FO(<, ≡) with the standard congruence predicates t ≡ 0 (mod n), for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FO(<, ≡)- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, respectively. We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies.

show abstract

Temporal Ontology-Mediated Queries and First-Order Rewritability: A Short Course

Cited by 3 publications

References 71 publications

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Finite Materialisability of Datalog Programs with Metric Temporal Operators

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

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