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    Therefore, the bijection between satisfying valuations an... — Carmelics
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    Challenges→3-SAT can be reduced to INDEPENDENT SET in polynomial time

    Therefore, the bijection between satisfying valuations and independent sets of size n breaks down in any non-bivalent semantic framework, limiting the reduction's logical generality.

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    Key Terms

    Bijection(in set theory and mathematics)
    A perfect one-to-one matching between two sets, where every element in one set pairs with exactly one element in the other, and nothing is left unpaired.
    Semantic framework(as the type of framework substitutional quantification represents)
    A system that explains what words and logical symbols actually mean and how they connect to reality or ideas.
    bivalent(used in logic to describe traditional systems that allow only two possible truth values)
    A system that uses exactly two values, typically true and false.
    independent sets(used in graph theory and logic to describe non-overlapping or non-interfering selections)
    A group of items selected from a larger collection where no two items in the group are directly connected or related to each other.

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    logical generality(used to describe how widely applicable a logical rule is)
    The degree to which a logical principle or rule works across different types of systems or situations without exceptions.
    reduction(Lambda calculus or term-rewriting systems)
    A computational process analogous to computing the value of a function, proceeding through a series of discrete calculation steps applied to a term
    satisfying valuations(used in formal logic to describe when truth assignments fulfill the requirements of a logical system)
    Assignments of true or false values to statements that make a logical formula work or come out true.

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    2 topics

    Truth & Knowledge1 linkedModality & Possibility1 linked

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    3-SAT can be reduced to INDEPENDENT SET in polynomial time

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