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    Van Benthem's correspondence theory shows that some S4-va... — Carmelics
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    Challenges→Compactness and Löwenheim-Skolem properties hold for modal logics K and S4.

    Van Benthem's correspondence theory shows that some S4-valid formulas correspond to non-elementary frame properties, which are invisible to the first-order many-sorted translation MS(4).

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    Key Terms

    First-order logic (MS(4))(as a simpler translation method that cannot capture some frame properties)
    A basic system for writing logical statements that can talk about individual things and their properties, but has limits on what it can express.
    Frame properties(in modal logic)
    Characteristics of the possible worlds and how they relate to each other in modal logic.
    Non-elementary(describing algorithm complexity)
    So computationally complex that it exceeds even exponential difficulty—essentially, impractically slow to solve.
    S4(as used in the statement)
    A specific system of modal logic with particular rules about how possibility and necessity work; it's named S4 just like a product model number.
    Valid formulas

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    (the focus of what the theorem proves)
    Statements written in the precise language of logic that are correctly formed and logically true—they follow the rules and make sense.
    Van Benthem(The statement refers to his work on correspondence theory)
    Johan van Benthem is a Dutch logician who studies how different logical systems work and relate to each other, particularly in modal logic and reasoning about knowledge.
    correspondence theory(philosophy of truth)
    A traditional monistic theory of truth that is often taken as exemplary of the monist approach

    Connections

    2 topics

    Proof of definition segments1 linkedModality & Possibility1 linked

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    Compactness and Löwenheim-Skolem properties hold for modal logics K and S4.

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