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    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that The truth-preserving map from relational models to the space of all types is usually not a modal bisimulation.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Brandenburger and Dekel (1993) showed that the universal type space is a complete representation of all belief hierarchies, preserving epistemic equivalence by construction.
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    • 2.If the type morphism is truth-preserving and the type space is universal, then modal equivalence is preserved as a consequence of the space's terminal object property.
      ?

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    • 3.The failure of bisimulation in non-universal type spaces reflects incompleteness of the model, not an intrinsic property of the type-state mapping.
      ?

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    Reason for 2 of 2
    ?
    • 1.Moss and Viglizzo's coalgebraic semantics demonstrates that for finitary modal logics, truth-preserving maps between Kripke models and type spaces can be shown to respect bisimilarity when the functor is a polynomial.
      ?

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    • 2.The claim conflates bisimulation failure for arbitrary relational models with a general impossibility, ignoring that restricted model classes do admit bisimulation-compatible type morphisms.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A full description of informational attitudes can be constructed by mapping states to types.
      ?

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    • 2.Such a mapping does not in general preserve the modal equivalence relations required for bisimulation.
      ?

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