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    In a many-valued logic (e.g., Łukasiewicz's three-valued ... — Carmelics
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    Challenges→3-SAT can be reduced to INDEPENDENT SET in polynomial time

    In a many-valued logic (e.g., Łukasiewicz's three-valued system), a literal can take an intermediate value, so 'at least one literal true per clause' fails to uniquely determine a valid independent set node.

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    Key Terms

    Many-valued logic(Contrasted with classical two-valued logic; shares with intuitionistic logic the failure of the law of excluded middle)
    A logical system that admits more than two truth values, introduced by Łukasiewicz in the 1920s
    Three-valued system(as used in logic)
    A logic system with exactly three possible truth values instead of two—typically true, false, and something in between (like 'unknown' or 'partially true').
    clause(in formal logic rules)
    One of several rules or conditions being listed; here it refers to different numbered rules (3-5) that could apply.
    independent set
    A set of vertices V' ⊆ V in a graph G = ⟨V, E⟩ such that no two vertices in V' are connected by an edge
    literal(propositional logic / conjunctive normal form)

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    A propositional variable p_k or its negation ¬p_k
    node(Extensive-form game theory)
    A decision or information point in a game tree representing a position a player may reach
    Łukasiewicz(the person being referenced for this logical discovery)
    A Polish logician (1878-1956) who made major contributions to logic and philosophy, particularly in studying how classical logic works and can be simplified.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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

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