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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that PDL's calculus is sound and complete only in the weak sense.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Weak completeness (every valid formula is provable) is the standard notion of completeness in propositional modal logic, making 'only' misleading.
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    • 2.Segerberg's original completeness proof for PDL establishes exactly what standard Hilbert-style axiomatizations are expected to establish.
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    • 3.The absence of strong completeness is a feature shared by virtually all normal modal logics with the Barcan formula or analogous infinitary commitments, not a deficiency unique to PDL.
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    Reason for 2 of 2
    ?
    • 1.Uncompactness entails failure of strong completeness but leaves weak completeness fully intact, so the two properties operate at distinct levels of logical strength.
      ?

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    • 2.Kozen and Parikh's 1981 completeness result for PDL is standardly cited in the literature as a genuine completeness theorem without qualification, undermining the rhetorical force of 'only'.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.PDL includes the induction axiom (Axiom 5)
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    • 2.The induction axiom is responsible for PDL being uncompact
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    • 3.Compactness fails for PDL
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