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    Propositional logic satisfiability is NP-complete — Carmelics
    Home/Philosophy of Language
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    Propositional logic satisfiability is NP-complete

    Modality & PossibilityPhilosophy of Language
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • Cook (1971) and Buss (1987) established that full propositional satisfiability is NP-complete
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.NP-completeness is defined relative to deterministic Turing machines, a model whose physical realizability remains philosophically contested (cf. Gandy 1980).
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    • 2.If alternative computational substrates (e.g., analog or quantum systems) collapse P and NP, SAT's 'hardness' is model-relative, not an intrinsic logical property.
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    • 3.Claims about propositional satisfiability complexity thus presuppose a contingent choice of computational ontology, not a necessary logical truth.
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    Reason against 2 of 2
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    • 1.Cook's theorem establishes NP-completeness under polynomial-time many-one reductions, but Buss's bounded arithmetic formalizes this within systems of varying proof-theoretic strength.
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    • 2.Whether NP-completeness proofs are themselves formalizable without presupposing consistency of strong arithmetical systems is an open foundational question (cf. Krajíček 1995).
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    • 3.The claim that SAT is NP-complete inherits the epistemic status of the metatheory in which complexity classes are defined, making it a conditional rather than absolute result.
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    Topics

    Philosophy of LanguageModality & Possibility

    Connections

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    Truth & Knowledge1 linked

    Related

    Claims about propositional satisfiability complexity thus presuppose a contingen...Cook (1971) and Buss (1987) established that full propositional satisfiability i...Cook's theorem establishes NP-completeness under polynomial-time many-one reduct...If alternative computational substrates (e.g., analog or quantum systems) collap...
    +3 moreShow less
    NP-completeness is defined relative to deterministic Turing machines, a model wh...The claim that SAT is NP-complete inherits the epistemic status of the metatheor...Whether NP-completeness proofs are themselves formalizable without presupposing ...

    Similar

    Validity and satisfiability problems for classical propositional logic...88%Cook (1971) and Buss (1987) established that full propositional satisf...87%Validity and satisfiability for modal logics S4 and S5 are PSPACE-comp...87%Validity and satisfiability problems for modal logics S4 and S5 are PS...84%

    Source

    AI-extracted1/3 agreementValid
    SEP: computational-complexity
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    It thus seems reasonable to summarize the current status of the \(\textbf{P} \neq \textbf{NP}\)? problem as follows: (i) \(\textbf{P} \neq \textbf{NP}\) is widely believed to be true on the basis of convergent inductive and heuristic evidence; (ii) we currently have no reason to suspect that this statement is formally independent of the mathematical theories which we accept in practice; but (iii) a proof \(\textbf{P} \neq \textbf{NP}\) is still considered to be beyond the reach of current techni
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit