Labelled Tableaux for Propositional Linear Time Logic Over Finite Frames

Cerrito, Serenella; Mayer, Marta Cialdea

doi:10.1007/978-94-011-4040-9_6

Cited by 4 publications

(8 citation statements)

References 5 publications

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“…Local reasoning for agent A discrete LTL. In this respect, the systems closest to ours are [7,18,30] (P.H. Schmitt and J. GoubaultLarrecq, Unpublished data).…”

Section: Related and Future Workmentioning

confidence: 60%

“…There are labelled systems for different temporal logics [7,18,19,24,29,30,35]. However, these are not for full 18.…”

Section: Related and Future Workmentioning

confidence: 99%

“…Schmitt and J. GoubaultLarrecq, Unpublished data). The [18] considers time points as labels for formulas, whereas [7,30] consider time intervals. Schmitt and Goubault-Larrecq employ constraint graphs to reason about completeness of their rules where labels are time intervals, similar to what we did for our time-point labels.…”

Section: Related and Future Workmentioning

confidence: 99%

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Labelled Tableaux for Distributed Temporal Logic

Basin¹,

Caleiro²,

Ramos³

et al. 2009

Journal of Logic and Computation

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The distributed temporal logic DTL is a logic for reasoning about temporal properties of discrete distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labelled tableaux system for full DTL. To achieve this, we first formalize a labelled tableaux system for reasoning locally at each agent and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL. We also provide examples illustrating the use of DTL and our tableaux system.

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“…Local reasoning for agent A discrete LTL. In this respect, the systems closest to ours are [7,18,30] (P.H. Schmitt and J. GoubaultLarrecq, Unpublished data).…”

Section: Related and Future Workmentioning

confidence: 60%

“…There are labelled systems for different temporal logics [7,18,19,24,29,30,35]. However, these are not for full 18.…”

Section: Related and Future Workmentioning

confidence: 99%

See 1 more Smart Citation

Labelled Tableaux for Distributed Temporal Logic

Basin¹,

Caleiro²,

Ramos³

et al. 2009

Journal of Logic and Computation

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“…A number of tableaux and other deductive systems have been given for fragments of LTL, e.g., [5,7,10,11,12,13,16,20,21,22,23,25,27] to name a few. In particular, different kinds of labels are employed to guide the proof search in the different labeled systems.…”

Section: Related and Future Workmentioning

confidence: 99%

“…In particular, different kinds of labels are employed to guide the proof search in the different labeled systems. For instance, [13] considers time points as labels for formulas, while [5,20,21] consider time intervals. It is interesting to note that Schmitt and Goubault-Larrecq employ constraint graphs to reason about the completeness of their rules, where labels are time intervals, similar to what we did for our time-point labels.…”

Section: Related and Future Workmentioning

confidence: 99%

A Labeled Tableaux System for the Distributed Temporal Logic DTL

Basin

Caleiro

Ramos

et al. 2008

2008 15th International Symposium on Temporal Representation and Reasoning

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DTL is a distributed temporal logic for reasoning about temporal properties of distributed systems from the local point of view of the system's agents, which are assumed to execute sequentially and to interact by means of synchronous event sharing. We present a sound and complete labeled tableaux system for future-time DTL. To achieve this, we first formalize a labeled tableaux system for reasoning locally at each agent, which provides a system for full future-time LTL, and afterwards we combine the local systems into a global one by adding rules that capture the distributed nature of DTL.

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A History of Until

Masini

Viganò

Volpe

2010

Electronic Notes in Theoretical Computer Science

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Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: AUB holds at the current time instant w iff either B holds at w or there exists a time instant w ′ in the future at which B holds and such that A holds in all the time instants between the current one and w ′ . This "ambivalent" nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the "history" of until, i.e., the "internal" universal quantification over the time instants between the current one and w ′ . This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new history operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until.

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Labelled Tableaux for Propositional Linear Time Logic Over Finite Frames

Cited by 4 publications

References 5 publications

Labelled Tableaux for Distributed Temporal Logic

Labelled Tableaux for Distributed Temporal Logic

A Labeled Tableaux System for the Distributed Temporal Logic DTL

A History of Until

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