Temporal and Modal Logic

Emerson, E. Allen

doi:10.1016/b978-0-444-88074-1.50021-4

Cited by 1,344 publications

(1,052 citation statements)

References 62 publications

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“…CTL* (Emerson, 1990) is an example of "branching-time" logic. Path quantifiers A ("for all paths") and E ("for some path") can prefix arbitrary combinations of linear time operators.…”

Section: Temporal Logicsmentioning

confidence: 99%

“…Formulas of Linear Temporal Logic (LTL) (Emerson, 1990) are built on top of a set Prop of atomic propositions using the standard Boolean operators, the unary temporal operator X (next), and the binary temporal operator U (until). In the following we assume to have a fixed set of atomic propositions Prop, and we define Σ = 2 Prop as the set of subsets of Prop.…”

Section: Temporal Logicsmentioning

confidence: 99%

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The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula ϕ, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.ϕ, which requires that the formula be satisfied for all execution paths, and the existential interpretation E.ϕ, which requires that the formula be satisfied for some execution path.When LTL is applied to the definition of goals in planning problems on nondeterministic domains, these two extreme cases are too restrictive. It is often impossible to develop plans that achieve the goal in all the nondeterministic evolutions of a system, and it is too weak to require that the goal is satisfied by some execution.In this paper we explore alternative interpretations of an LTL formula that are between these extreme cases. We define a new language that permits an arbitrary combination of the A and E quantifiers, thus allowing, for instance, to require that each finite execution can be extended to an execution satisfying an LTL formula (AE.ϕ), or that there is some finite execution whose extensions all satisfy an LTL formula (EA.ϕ). We show that only eight of these combinations of path quantifiers are relevant, corresponding to an alternation of the quantifiers of length one (A and E), two (AE and EA), three (AEA and EAE), and infinity ((AE) ω and (EA) ω ). We also present a planning algorithm for the new language that is based on an automata-theoretic approach, and study its complexity.

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“…CTL* (Emerson, 1990) is an example of "branching-time" logic. Path quantifiers A ("for all paths") and E ("for some path") can prefix arbitrary combinations of linear time operators.…”

Section: Temporal Logicsmentioning

confidence: 99%

Section: Temporal Logicsmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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“…Time is ubiquitous in information systems, but the mode of representation/perception varies in function of the purpose of the analysis [18], [19]. Firstly, there is a choice of a temporal ontology, which can be based either on time points (instants) or on intervals (periods).…”

Section: The Formalism Of Temporal Rulesmentioning

confidence: 99%

Classification Rules + Time = Temporal Rules

Cotofrei

Stoffel

2002

Lecture Notes in Computer Science

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Abstract. Due to the wide availability of huge data collection comprising multiple sequences that evolve over time, the process of adapting the classical data-mining techniques, making them capable to work into this new context, becomes today a strong necessity. In [1] we proposed a methodology permitting the application of a classification tree on sequential raw data and the extraction of the rules having a temporal dimension. In this article, we propose a formalism based on temporal first logic-order and we review the main steps of the methodology through this theoretical frame. Finally, we present some solutions for a practical implementation.

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“…We assume familiarity with the standard logics used in verification: LTL, CTL, Hennessy-Milner Logic (HML), the modal µ-calculus (see [20,13,4]). …”

Section: Parameterized Complexity Of Non-flat Temporal Logic Model Chmentioning

confidence: 99%

A Parametric Analysis of the State Explosion Problem in Model Checking

2002

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In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for non-flat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust.

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Temporal and Modal Logic

Cited by 1,344 publications

References 62 publications

The Planning Spectrum - One, Two, Three, Infinity

The Planning Spectrum - One, Two, Three, Infinity

Classification Rules + Time = Temporal Rules

A Parametric Analysis of the State Explosion Problem in Model Checking

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