Questions tagged [kripke-models]

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Proving Gabbay rule for Modal Logic

I'm currently working on exercises of the book "Modal Logic" by A.Chagrov and M.Zakharyaschev (for pleasure, not homework). One exercise asks to prove this version of Gabbay rule (exercise $3.10$): A ...
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characterization of non-reflexive Kripke frames

Can the class of non-reflexive (that is not being reflexive of course) be characterized with a set of modal formulae? What about irreflexive (having only non-reflexive points)?
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Understanding The First Axiom Of Gödel's Ontological Proof

On Wikipedia, the first Axiom of Gödel's ontological proof is $$(P(\phi)\land\square\forall x(\phi(x)\Rightarrow\psi(x)))\Rightarrow P(\psi),$$ I assume there are implicit quantifiers present for $\...
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Different ways to define Kripke structure

The Wikipedia page https://en.wikipedia.org/wiki/Kripke_structure_(model_checking)#Example has an example of a Kripke structure $M = (S,R,L)$; however, others define Kripke structures as $M = (S,R,V)$ ...
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Proving the Glivenko theorem via Kripke models

We'll prove it in just one direction, since the other one is obvious. So, assume $\psi$ is a theorem of classical propositional logic. Prove that $\lnot \lnot \psi$ is a theorem of intuitionistic ...
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How to show that someone beleive someone don't beleive $\phi$ with Kripke models?

I want to model a logic of beliefs with two agents where : $$M,w^*⊨\phi\wedge Ba\phi\wedge Bb\neg\phi\wedge BaBb\neg\phi$$ I think I'm using Kripke semantics. I think that i.e. it describe a world ...
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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\...
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What is the Upper-Bound for a Kripke Model in Normal Modal Logics?

I am currently looking for a paper for a proof about the upper-bound on the size of a Kripke model in modal logic, no matter the axiom considered. I am considering only the propositional modal logic ...