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    Moss and Viglizzo's coalgebraic semantics demonstrates th... — Carmelics
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    Challenges→The truth-preserving map from relational models to the space of all types is usually not a modal bisimulation.

    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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    Key Terms

    Bisimilarity(the property maps must respect)
    A relation between two logical systems or structures that captures whether they behave identically from every logical perspective, even if they're structured differently.
    Coalgebraic semantics(the formal framework being described)
    A mathematical approach to understanding meaning and truth that uses abstract structures called coalgebras, which are useful for studying systems that evolve or change over time.
    Finitary modal logics(the type of logical system being analyzed)
    Systems of logic that study concepts like 'possibly' and 'necessarily' while only using a finite number of basic operations or rules.
    Kripke models(one of the mathematical structures discussed)
    A formal way of representing logical possibility, where possible worlds are connected by relationships, and something is true based on which worlds you consider.

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    Moss and Viglizzo(authors of the semantic framework discussed)
    Contemporary logicians and mathematicians who developed new ways to formally study how meaning works in logical systems.
    Polynomial functor(the condition required for the theorem to work)
    A specific type of mathematical transformation built from simple pieces in a way that's analogous to polynomial equations in algebra.
    Truth-preserving maps(the key property being examined)
    Functions or connections between logical systems that guarantee if something is true in one system, it remains true when translated to another system.
    Type spaces(the other main mathematical structure discussed)
    A mathematical structure that represents all the different possible types or categories something could belong to, organized in a systematic way.
    functor(Leśniewski's formal syntax for logical languages)
    A combining expression that precedes a parenthesized sequence of argument expressions in Leśniewski's logical languages

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    2 topics

    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    The truth-preserving map from relational models to the space of all types is usu...

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