Interval temporal logics over strongly discrete linear orders: Expressiveness and complexity

Bresolin, Davide; Monica, Dario Della; Montanari, Angelo; Sala, Pietro; Sciavicco, Guido

doi:10.1016/j.tcs.2014.03.033

Cited by 22 publications

(23 citation statements)

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“…A systematic study of their expressive power and computational complexity resulted in a nearly complete classification. It was proved that the easiest fragments are NP-complete, whereas the other are PSpace-complete, NExpTime-complete, ExpSpace-complete, or undecidable [11,21]. Other ways of restricting the Halpern-Shoham logic consist for example in weakening the definitions of relations interpreting the modal operators, and imposing additional constraints on the flow of time (for example, discreteness or density) [3,14,7].…”

Section: Reflexive Framesmentioning

confidence: 99%

“…As a result, restrictions on HS have been intensively investigated in order to identify fragments of relatively low computational complexity, whose expressive power is high enough for a variety of applications. A number of methods to specify HS-fragments have been proposed, for example, restricting the set of modal operators occurring in the language [9,10,11], softening semantics of modal operators [12], and restricting the nesting-depth of modal operators [13].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid fragments of Halpern–Shoham logic and their expressive power

Wałęga¹

2019

Theoretical Computer Science

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Halpern and Shoham modal logic of time intervals (HS in short) is an elegant and highly influential propositional interval-based modal logic. Its sub-propositional fragments, that is fragments obtained by restricting use of propositional connectives, and their hybrid extensions with nominals and satisfaction operators have been recently studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. In particular, we (1) compare classes of frames definable in full HS and in its hybrid extension, and (2) determine in which sub-propositional HS-fragments we can express the difference operator, nominals, and satisfaction operators. The obtained results enable us to classify HS, its sub-propositional fragments, and their hybrid extensions according to their expressive power.

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Section: Reflexive Framesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hybrid fragments of Halpern–Shoham logic and their expressive power

Wałęga¹

2019

Theoretical Computer Science

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“…In fact, interval temporal logics are highly expressive, often undecidable formalisms whose detailed classification has occupied researchers up until recent years [7]. Only recently have real-time interval temporal logics been studied in some detail [9,39]. Some interval logics, such as propositional neighborhood logic, remain decidable over the reals [41].…”

Section: Other Real-time Logicsmentioning

confidence: 99%

“…Proof We reduce the finite counter problem of counter machines (Section 5.1) to describe all valid computations of M that halt; that is, in particular, all computations that do not get stuck forever in the initial loop (4) that increments v x . 9 Finally consider the decision problem BV ∃ R ≥0 , ω, c ( ). If its answer is YES, we claim that there are finitely many models that satisfy .…”

Section: Lemma 25 Bvmentioning

confidence: 99%

Bounded variability of metric temporal logic

Furia

Spoletini

2016

Ann Math Artif Intell

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Deciding validity of Metric Temporal Logic (MTL) formulas is generally very complex and even undecidable over dense time domains; bounded variability is one of the several restrictions that have been proposed to bring decidability back. A temporal model has bounded variability if no more than v events occur over any time interval of length V , for constant parameters v and V. Previous work has shown that MTL validity over models with bounded variability is less complex-and often decidable-than MTL validity over unconstrained models. This paper studies the related problem of deciding whether an MTL formula has intrinsic bounded variability, that is whether it is satisfied only by models with bounded variability. The results of the paper are mainly negative: over dense time domains, the problem is mostly undecidable (even if with an undecidability degree that is typically lower than deciding validity); over discrete time domains, it is decidable with the same complexity as deciding validity. As a partial complement to these negative results, the paper also identifies MTL fragments where deciding bounded variability is simpler than validity, which may provide for a reduction in complexity in some practical cases.

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“…PNL has only two modalities ⟨ ⟩ and ⟨ ⟩ corresponding to Allen's relations meets and met by, respectively. Unlike HS and most of its fragments, the satisfiability problem for PNL is decidable [10]. Moreover, when interpreted over discrete linear orders, PNL can be easily extended with metric capabilities.…”

Section: Preliminariesmentioning

confidence: 99%

Ultimately-periodic Interval Model Checking for Temporal Dataset Evaluation

Monica¹,

Montanari²,

Murano³

et al.

EPiC Series in Computing

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Temporal dataset evaluation is the problem of establishing to what extent a set of temporal data (histories) complies with a given temporal condition. Checking interval temporal logic formulas against a finite model has been recently proposed, and proved successful, as a tool to solve such a problem. In this paper, we address the problem of checking interval temporal logic specifications, supporting interval length constraints, against infinite, finitely representable models, and we show the applicability of the resulting procedure to the evaluation of incomplete temporal datasets viewed as finite prefixes of ultimately-periodic histories.

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Interval temporal logics over strongly discrete linear orders: Expressiveness and complexity

Cited by 22 publications

References 10 publications

Hybrid fragments of Halpern–Shoham logic and their expressive power

Hybrid fragments of Halpern–Shoham logic and their expressive power

Bounded variability of metric temporal logic

Ultimately-periodic Interval Model Checking for Temporal Dataset Evaluation

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