An axiomatization of PCTL

Mark Reynolds

    Research output: Contribution to journal › Article

    26 Citations (Scopus)

    Abstract

    A sound and complete axiomatization for a computation tree logic with past operators, PCTL*, is given. The logic extends the standard branching time logic CTL* of R-generable models via the use of past-time operators and semantics based on a finite linear past leading back from any point in any fullpath. Furthermore, the valid formulas of CTL* are also valid in PCTL*. The past operators allow us to avoid use of any unusual rules of inference such as the ugly automata-motivated AA rule which is part of the existing complete axiomatization for CTL*. (c) 2005 Elsevier Inc. All rights reserved.
    Original languageEnglish
    Pages (from-to)72-119
    JournalInformation and Computation
    Volume201
    DOIs
    Publication statusPublished - 2005

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    Trees (mathematics)
    Axiomatization
    Mathematical operators
    Semantics
    Acoustic waves
    Logic
    Valid
    Time Operator
    Operator
    Automata
    Branching
    Model

    Cite this

    Reynolds, Mark. / An axiomatization of PCTL. In: Information and Computation. 2005 ; Vol. 201. pp. 72-119.
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    Reynolds, M 2005, 'An axiomatization of PCTL' Information and Computation, vol. 201, pp. 72-119. https://doi.org/10.1016/j.ic.2005.03.005

    An axiomatization of PCTL. / Reynolds, Mark.

    In: Information and Computation, Vol. 201, 2005, p. 72-119.

    Research output: Contribution to journal › Article

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    AB - A sound and complete axiomatization for a computation tree logic with past operators, PCTL*, is given. The logic extends the standard branching time logic CTL* of R-generable models via the use of past-time operators and semantics based on a finite linear past leading back from any point in any fullpath. Furthermore, the valid formulas of CTL* are also valid in PCTL*. The past operators allow us to avoid use of any unusual rules of inference such as the ugly automata-motivated AA rule which is part of the existing complete axiomatization for CTL*. (c) 2005 Elsevier Inc. All rights reserved.

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    JO - Information and Computation

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    SN - 0890-5401

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    Reynolds M. An axiomatization of PCTL. Information and Computation. 2005;201:72-119. https://doi.org/10.1016/j.ic.2005.03.005

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