Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    The truth-preserving map from relational models to the sp... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Philosophy of Language
    HistoryEditSee Inverse

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

    Modality & PossibilityPhilosophy of Language
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

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

      Think about whether this reason is strong or weak

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

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

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

      Think about whether this reason is strong or weak

    Reason against 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    Philosophy of LanguageModality & Possibility

    Connections

    1 topic

    Truth & Knowledge1 linked

    Related

    A full description of informational attitudes can be constructed by mapping stat...Brandenburger and Dekel (1993) showed that the universal type space is a complet...If the type morphism is truth-preserving and the type space is universal, then m...Moss and Viglizzo's coalgebraic semantics demonstrates that for finitary modal l...
    +3 moreShow less
    Such a mapping does not in general preserve the modal equivalence relations requ...The claim conflates bisimulation failure for arbitrary relational models with a ...The failure of bisimulation in non-universal type spaces reflects incompleteness...

    Similar

    This mapping preserves truth across the relational model.81%The space of all epistemic types is universal in the sense that every ...80%Such a mapping does not in general preserve the modal equivalence rela...78%De re modal truths are grounded in facts about counterparts, not in a ...73%

    Source

    AI-extracted1/3 agreementValid
    SEP: logics-for-games
    View source passageHide passage
    To fix all of the agents’ beliefs, the analysis moves to types \(\mathfrak{f}=\langle f_0,f_1,\ldots\rangle\), containing some \(f_n\) for every natural number n. In this extended framework the situation becomes more complicated. The space of all such types is universal in the following sense: every relational model can be mapped in a truth-preserving manner to the space of all types by sending each state to a full description of the agents’ corresponding first- and higher-order informational at
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit