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    Weak completeness (every valid formula is provable) is th... — Carmelics
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    Challenges→PDL's calculus is sound and complete only in the weak sense.

    Weak completeness (every valid formula is provable) is the standard notion of completeness in propositional modal logic, making 'only' misleading.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Weak completeness (valid → provable) is achieved by major modal logics K, T, S4, S5, making it the standard in textbooks and research.
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    • 2.Strong completeness (Γ ⊨ φ → Γ ⊢ φ) fails for infinitary cases in modal logic, so weak completeness is the realistic standard.
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    • 3.Using 'only' suggests weak completeness is unusual or limited, when it's actually the primary completeness notion modal logicians establish.
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    Reasons Against

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    Reason against
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    • 1.Strong completeness is provable for K, T, S4, S5 with finite axiomatizations, so 'only weak' undersells what modal logic actually achieves.
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    • 2.The word 'only' reasonably flags that weak completeness omits finite consistency preservation, a philosophically significant limitation.
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    • 3.Pedagogically, distinguishing weak from strong completeness clarifies what's proven, even if weak is standard—'only' aids precision, not misleading.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    PDL's calculus is sound and complete only in the weak sense.Pedagogically, distinguishing weak from strong completeness clarifies what's pro...Strong completeness (Γ ⊨ φ → Γ ⊢ φ) fails for infinitary cases in modal logic, s...Strong completeness is provable for K, T, S4, S5 with finite axiomatizations, so...
    +3 moreShow less
    The word 'only' reasonably flags that weak completeness omits finite consistency...Using 'only' suggests weak completeness is unusual or limited, when it's actuall...Weak completeness (valid → provable) is achieved by major modal logics K, T, S4,...

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    2 (1 for, 1 against)
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    1 edit