A Road Map of Interval Temporal Logics and Duration Calculi

Goranko, Valentin; Montanari, Angelo; Sciavicco, Guido

doi:10.3166/jancl.14.9-54

Cited by 125 publications

(92 citation statements)

References 49 publications

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“…Considering now, again, BBLL and its fragments, as in the finite case we can prove that NPcompleteness of BB [43] can be extended to it. Since the satisfiability problem for propositional logic is NP-complete, that for every proper fragment of BBLL including it is at least NP-hard.…”

Section: Np-completenessmentioning

confidence: 99%

“…We can prove that the NP-membership of BB [43] can be extended to BBLL. Since the satisfiability problem for propositional logic is itself NP-complete, BBLL and its fragments are NPcomplete.…”

Section: Np-completenessmentioning

confidence: 99%

“…From [43], we know that BB (and thus also its fragments B and B) is NP-complete. We can prove that the NP-membership of BB [43] can be extended to BBLL.…”

Section: Np-completenessmentioning

confidence: 99%

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Reasoning with Time Intervals: A Logical and Computational Perspective

Sciavicco

2012

ISRN Artificial Intelligence

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The role of time in artificial intelligence is extremely important. Interval-based temporal reasoning can be seen as a generalization of the classical point-based one, and the first results in this field date back to Hamblin (1972) and Benhtem (1991) from the philosophical point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one. Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past ten years and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.

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Section: Np-completenessmentioning

confidence: 99%

Section: Np-completenessmentioning

confidence: 99%

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Reasoning with Time Intervals: A Logical and Computational Perspective

Sciavicco

2012

ISRN Artificial Intelligence

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“…We will not consider interval temporal logics in this chapter and refer the interested reader to (Vilain et al, 1989;Blackburn, 1992;Gabbay et al, 2000;Goranko et al, 2004).…”

Section: Remark 119mentioning

confidence: 99%

Spatial Logic + Temporal Logic = ?

Kontchakov

Kurucz

Wolter

et al. 2007

Handbook of Spatial Logics

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IntroductionAs follows from the title of this chapter, our primary aim is to analyse possible solutions to the equationwhere the items on the left-hand side are some standard spatial and temporal logics, and + is some 'operator' combining these two logics into a single one. The question we are concerned with is how the computational complexity and the expressive power of the component logics are related to the complexity and expressiveness of the resulting spatio-temporal logic x under various combination operators +.

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“…As for temporal individuals, time instants can be replaced with time intervals (equivalently, periods or stretches of time) connected by (a subset of) Allen's relations before, meets, overlaps, starts, during, equal, and finishes, and their inverses or suitable combinations [GMS04]. As in the case of instant-based domains, we may distinguish between discrete and dense domains, bounded and unbounded domains, linear, branching, and circular domains, and so on.…”

Section: Definitionmentioning

confidence: 99%