Tractable Interval Temporal Propositional and Description Logics

Artale, Alessandro; Kontchakov, Roman; Ryzhikov, Vladislav; Zakharyaschev, Michael

doi:10.1609/aaai.v29i1.9406

Cited by 14 publications

(5 citation statements)

References 27 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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“…• for any pure-past formula φ of LTL+P, it is possible to build directly an equivalent deterministic finite automaton of singly exponential size with respect to the size of φ, without the need of a subsequent determinization step; thanks to this fact, the reactive synthesis problem for the pure-past fragment of LTL+P is only EXPTIMEcomplete (Artale et al 2023b);…”

Section: Reactive Synthesismentioning

confidence: 99%

Linear Temporal Logic Modulo Theories over Finite Traces

Heyninck

Kern-Isberner

Meyer

2022

Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence

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Lexicographic inference is a well-known and popular approach to reasoning with non-monotonic conditionals. It is a logic of very high-quality, as it extends rational closure and avoids the so-called drowning problem. It seems, however, this high quality comes at a cost, as reasoning on the basis of lexicographic inference is of high computational complexity. In this paper, we show that lexicographic inference satisfies syntax splitting, which means that we can restrict our attention to parts of the belief base that share atoms with a given query, thus seriously restricting the computational costs for many concrete queries. Furthermore, we make some observations on the relationship between c-representations and lexicographic inference, and reflect on the relation between syntax splitting and the drowning problem.

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“…Related Work. Apart from the above references, we want to point out work on combining DLs with Halpern and Shoham's interval logic [3,4]. This setting is quite different from ours, since it uses intervals (rather than time points) as the basic time units.…”

Section: Introductionmentioning

confidence: 98%

“…To overcome the problem that pure DLs are not able to express such temporal patterns, a great variety of temporal extensions of DLs have been investigated in the literature. 3 In the present paper, we concentrate on the DL ALC and combine it with linear temporal logic (LTL), a point-based temporal logic whose semantics assumes a linear flow of time. But even if these two logics are fixed, there are several other design decisions to be made.…”

Section: Introductionmentioning

confidence: 99%

“…Basically, this allows one to state that elements belonging to a concept need to belong to that concept for at least k consecutive time points, and similarly for roles. For example, according to the WHO, patients with paucibacillary leprosy should receive MDT as treatment for 6 consecutive months, 4 which can be expressed by making the role getMDTagainstPB rigid for 6 time points (assuming that each time point represents one month). In Section 4, we consider the effect of adding interval-rigid concepts and roles as well as metric temporal operators to the logic ALC-LTL of [9], where temporal operators can only be applied to axioms.…”

Section: Introductionmentioning

confidence: 99%

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Metric Temporal Description Logics with Interval-Rigid Names

Baader

Borgwardt

Koopmann

et al. 2020

ACM Trans. Comput. Logic

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In contrast to qualitative linear temporal logics, which can be used to state that some property will eventually be satisfied, metric temporal logics allow us to formulate constraints on how long it may take until the property is satisfied. While most of the work on combining description logics (DLs) with temporal logics has concentrated on qualitative temporal logics, there is a growing interest in extending this work to the quantitative case. In this article, we complement existing results on the combination of DLs with metric temporal logics by introducing interval-rigid concept and role names. Elements included in an interval-rigid concept or role name are required to stay in it for some specified amount of time. We investigate several combinations of (metric) temporal logics with A ℒ C by either allowing temporal operators only on the level of axioms or also applying them to concepts. In contrast to most existing work on the topic, we consider a timeline based on the integers and also allow assertional axioms. We show that the worst-case complexity does not increase beyond the previously known bound of 2-E xp S pace and investigate in detail how this complexity can be reduced by restricting the temporal logic and the occurrences of interval-rigid names.

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Tractable Interval Temporal Propositional and Description Logics

Abstract: We design a tractable Horn fragment of the Halpern-Shoham temporal logic and extend it to interval-based temporal description logics, instance checking in which is P-complete for both combined and data complexity.

Cited by 14 publications

References 27 publications

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Finite Materialisability of Datalog Programs with Metric Temporal Operators

Linear Temporal Logic Modulo Theories over Finite Traces

Metric Temporal Description Logics with Interval-Rigid Names

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