# Questions tagged [kripke-models]

This tag is for questions relating to "Kripke’s models" for modal logic (or variants thereof) are the basis for many modern approaches to reasoning about knowledge and belief. For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non­classical logics.

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### How to prove that a formula is intuitionistically valid using Kripke semantics?

I want to know how to use Kripke semantics so that I can prove that a formula is intuitionistically valid. I think that all others cases will clear out if I understand the case of implication. Let's ...
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### Intuitionistic proof of $((p\rightarrow q)\rightarrow p)\rightarrow\neg \neg p$

I need to prove that the $\psi=((p\rightarrow q)\rightarrow p)\rightarrow\neg \neg p$ is intuitionistically valid. I tried using the topology of open sets of $\mathbb{R}$ and an arbitrary valuation, ...
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### Minimal Modal Logic and the Class of all Kripke Models

It's well known that minimal modal logic (i.e. propositional tautologies and axiom $K$ together with modus ponens and necessitation rule) captures the validities of the semantic class of all Kripke ...
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### Church-Rosser property and normal modal logic

I am trying to prove soundness and completeness for S4.2 and I am considering Kripke frames which are reflexive, transitive and have the Church-Rosser property. Now, there is one thing that really ...
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### Modal logic Box and diamond T

I didn't understand what is mean Box T, diamond T in this example: what is mean box True exist in world v?
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I cannot find an example for an invalid $S5$ formula $\psi$ (i.e. $\nvDash\psi$), such that $\diamond\psi$ is valid (i.e. $\vDash\diamond\psi$). If there is none, then $\vDash\diamond\psi\Rightarrow\,\... 1 vote 0 answers 270 views ### I am looking for a soundness, completeness and consistency proof for this particular$S5$calculus. I know that it suffices to add the axioms$(T)~\square\psi\rightarrow\psi(K)~\square(\psi\rightarrow\varphi)\rightarrow(\square\psi\rightarrow\square\varphi)(5)~\diamond\psi\rightarrow\square\...
In Harel's book on PDL (Propositional Dynamic Logic) I've learnt that Kripke frames are pairs such as: K = (K; $m_k$) Where $K$ is a set called states and $m_k$ is a meaning function assigning ...