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    Carmelics

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    Inverse View

    It is not the case that The reverse deductive correspondence holds: translations that are theorems of MSL correspond to theorems of the modal calculus.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The canonical model construction presupposes completeness of the base modal calculus, which fails for some normal modal logics (e.g., certain logics above S4).
      ?

      Think about whether this reason is strong or weak

    • 2.If the modal calculus is incomplete with respect to Kripke semantics, the canonical model B_K cannot faithfully represent all theorems, breaking the correspondence.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Many-sorted logic translations collapse intensional distinctions when modal operators are encoded as predicates over sort-restricted domains (cf. Fitting's concerns about intensional contexts).
      ?

      Think about whether this reason is strong or weak

    • 2.A formula provable in MSL via extensional reasoning about sorted domains may not correspond to a genuinely modal theorem but to an artifact of the translation scheme.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The canonical model B_K (or B_S4) can be used to build the general structure B_K𝔊 (or B_S4𝔊)
      ?

      Think about whether this reason is strong or weak

    • 2.The translation of a modal formula φ is true at a world of this general structure if and only if φ belongs to that world
      ?

      Think about whether this reason is strong or weak

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