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    If the background logic used to establish the entailment ... — Carmelics
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    Challenges→A polynomial time algorithm for any single NP-complete problem would entail the existence of polynomial time algorithms for all problems in NP.

    If the background logic used to establish the entailment is proof-theoretically stronger than the system modeling computation, the modal force of 'would entail' is theory-relative, not absolute.

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    Key Terms

    entailment(Conceptualist framework)
    Understood in terms of truth at a world
    modal force(as used in modal logic)
    The power or strength of a statement about necessity, possibility, or contingency—what makes something 'must be' versus 'might be'.
    proof-theoretically stronger(as used in mathematical logic)
    A system of logic that can prove more things or uses more powerful rules than another system—think of it as a more capable toolkit for demonstrating that statements are true.
    system modeling computation(as used in logic and computer science)
    A set of rules and methods designed to describe how computers process information and solve problems.
    theory-relative(as used in philosophy of logic)

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    Proof of definition segments1 linkedModality & Possibility1 linked

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    A polynomial time algorithm for any single NP-complete problem would entail the ...

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