Bounded Model Search in Linear Temporal Logic and Its Application to Planning

Cerrito, Serenella; Mayer, Marta Cialdea

doi:10.1007/3-540-69778-0_18

Cited by 18 publications

(15 citation statements)

References 10 publications

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“…Most of these approaches (Bacchus & Kabanza, 1998Calvanese et al, 2002;Cerrito & Mayer, 1998;de Giacomo & Vardi, 1999;Kvarnström & Doherty, 2001) use linear temporal logics as the goal language, and are not able to express conditions on the degree in which the goal should be satisfied with respect to the nondeterminism in the execution. Notable exceptions are the works described by Pistore, Bettin, and Traverso (2001), and by Dal Lago et al (2002).…”

Section: Related Work and Concluding Remarksmentioning

confidence: 99%

“…Quite often practical applications require plans that deal with goals that are more general than sets of final states. Several planning approaches have been recently proposed, where temporal logic formulas are used as goal language, thus allowing for goals that define conditions on the whole plan execution paths, i.e., on the sequences of states resulting from the execution of plans (Bacchus & Kabanza, 1998Calvanese, de Giacomo, & Vardi, 2002;Cerrito & A path quantifier is a (finite or infinite) word on alphabet {A, E}. The path quantifier can be seen as the definition of a two-player game for the selection of the outcome of action execution.…”

Section: Introductionmentioning

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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Section: Related Work and Concluding Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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“…Unlike the above-described implicit methods, the labeled tableau systems for LTL[F] and for PLTL over bounded models, respectively developed by Schmitt and GoubaultLarrecq [29] and by Cerrito and Cialdea-Mayer [5], employ a mechanism for labelling formulas with temporal constraints somewhat similar to ours.…”

Section: Point-based Linear and Branching Temporal Logicsmentioning

confidence: 98%

“…A labeled tableau system for the LTL-fragment LTL[F] has been proposed by Schmitt and Goubault-Larrecq [29] (an attempt to extend it to full LTL is reported in [30]). Finally, a tableau method for PLTL over bounded models has been developed by Cerrito and Cialdea-Mayer [5] (in [6], Cerrito et al generalize the method to first-order PLTL). The satisfiability problem for LTL and PLTL is PSPACE-complete [31], while that for PLTL over bounded models of polynomial length and LTL[F] is NP-complete [5,31].…”

Section: Point-based Linear and Branching Temporal Logicsmentioning

confidence: 99%

“…These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, e.g., [5,9,18,29,33], not much work has been done on tableau methods for intervalbased temporal logics. One reason for this disparity is that operators of interval temporal logics are in many respects more difficult to deal with.…”

Section: Introductionmentioning

confidence: 99%

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A general tableau method for propositional interval temporal logics: Theory and implementation

Goranko

Montanari

Sala

et al. 2006

Journal of Applied Logic

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In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's CDT logic interpreted over partial orders (BCDT + for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. ✩ This paper is an extended and revised version of [V. Goranko, A. Montanari, G. Sciavicco, A general tableau method for propositional interval temporal logics, in:

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2011

An Introduction to Practical Formal Methods Using Temporal Logic

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Bounded Model Search in Linear Temporal Logic and Its Application to Planning

Cited by 18 publications

References 10 publications

The Planning Spectrum - One, Two, Three, Infinity

The Planning Spectrum - One, Two, Three, Infinity

A general tableau method for propositional interval temporal logics: Theory and implementation

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