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
    An Extensionality Axiom is added to ΔK to give it a secon... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Part of a larger discussion

    Supports→The class 𝔊 of general structures built on modal structures can be axiomatized for minimal modal logic K.

    An Extensionality Axiom is added to ΔK to give it a second-order appearance

    Modality & PossibilityProof of definition segments
    ?Rate how convincing each reason is below to see the overall strength.

    No one has weighed in yet. Be the first to share reasons for or against this statement.

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

    Topics

    Modality & PossibilityProof of definition segments

    Related

    A theory ΔK can be defined using a Comprehension Axiom over many-sorted formulas...The class 𝔊 of general structures built on modal structures can be axiomatized ...

    Similar

    Next step

    Based on where you are in your exploration

    Browse more in Modality & Possibility
    Related propositions within the same area of thought.
    Hume's Principle can be consistently added to second-order logic78%The addition of Basic Law V to second-order logic implies a contradict...75%FACTORIZATION is in both NP and coNP.74%EXP and NEXP both properly extend P.72%

    Source

    AI-extracted
    SEP: logic-many-sorted
    View source passageHide passage
    Given a Kripke structure \[\mathcal{A}=\langle \mathbf{W},\mathbf{R},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] we say that \(\mathcal{AG}\) is a general structure built on \(\mathcal{A}\) if and only if \[\mathcal{AG}=\langle \mathbf{W},\mathbf{W}^{\prime },\mathbf{R},\epsilon _{1}^{\mathcal{A}},\langle P^{\mathcal{A}}\rangle _{P\in \Atom}\rangle\] where \(\Def \subseteq \mathbf{W}^{\prime }\subseteq \wp (\mathbf{W})\). [22] It can be proved that the set of worlds where a moda

    Details

    Type
    premise
    Perspectives
    0 (0 for, 0 against)
    Edits
    1 edit

    Open for perspectives

    This idea is waiting for its first supporting or challenging perspective.

    Share the first perspective