A Labeled Natural Deduction System for a Fragment of CTL *

Masini, Andrea; Viganò, Luca; Volpe, Marco

doi:10.1007/978-3-540-92687-0_23

Cited by 4 publications

(3 citation statements)

References 21 publications

(40 reference statements)

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“…First, the "recipe" for dealing with until that we gave here is abstract and general, and thus provides the basis for formalizing deduction systems for temporal logics endowed with U, both linear and branching time. We are currently considering CTL * and its sublogics as in [16,18] and are also working at a formal characterization of the class of logics that can be captured with our approach. Second, the well-behaved nature of our approach, where each connective and operator has one introduction and one elimination rule, paves the way to a prooftheoretical analysis of the resulting natural deduction systems, e.g., to show proof normalization and other useful meta-theoretical properties, which we are tackling in current work.…”

Section: Discussionmentioning

confidence: 99%

“…These operators have a local nature, in the sense that they speak not about sequences of time instants but about single time instants. Still, we can easily give natural deduction rules for them by generalizing the more standard "singletime instant" rules (e.g., [1,2,12,16,21,22,23]) using our labeling with sequences of time instants. As we will discuss in more detail below, if we collapse the sequences of time instants to consider only the final time instant in the sequence (or, equivalently, if we simply ignore all the instants in a sequence but the last), then these rules reduce to the standard ones.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A History of Until

Masini

Viganò

Volpe

2010

Electronic Notes in Theoretical Computer Science

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“…Still, we can easily give natural deduction rules for them by generalizing the more standard "single-time instant" rules (e.g., (Basin et al, 2009;Bolotov et al, 2007;Goré, 1999;Masini et al, 2009;Simpson, 1994;Viganò, 2000;Viganò & Volpe, 2008)) using our labeling with sequences of time instants. These 244 JANCL -20/2010.…”

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confidence: 99%

Back from the future

Masini

Vigano

Volpe

2010

Journal of Applied Non-Classical Logics

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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 N(LTL ∇ ) for a linear-time logic LTL ∇ endowed with the new history operator. We show that LTL ∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL ∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL ∇ formulas.

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A Tableau for the Combination of CTL and BCTL

McCabe-Dansted

2012

2012 19th International Symposium on Temporal Representation and Reasoning

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A Labeled Natural Deduction System for a Fragment of CTL *

Cited by 4 publications

References 21 publications

A History of Until

A History of Until

Back from the future

A Tableau for the Combination of CTL and BCTL

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