# Questions tagged [kripke-models]

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37 questions
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### How to prove in K $\vdash_{p \rightarrow \lozenge \square p} (\square p \rightarrow \lozenge p)$?

Let us denote $C$ the modal system obtained by adding the axiom $\alpha \rightarrow \lozenge \square \alpha$ to the axiom $K$ and all the propositional tautologies. As said in the title, I'm looking ...
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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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### Proving $\lnot \lnot (\psi \lor \lnot \psi)$ is a theorem of intuitionistic propositional logic

Here, $\psi$ is some arbitrary formula. The proof I've come up with is as follows. Assume $\lnot \lnot (\psi \lor \lnot \psi)$ is not a theorem of IPL, which means there exists some Kripke model ...
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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 ...
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### Determine a modal logic formula which a connective that is not valid but is true

I'm trying to understand how a formula can not be valid but also true in the above question.
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### Counter examples in modal logic

As I'm new to modal logic, I wanted to check whether my counter examples for the given formula is right. $$\Box A \rightarrow \Diamond B \Rightarrow \Box(\Box A \rightarrow \Diamond B)$$ First I ...
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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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### 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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### Proove that all finite non-standard Kripke frames are standard

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 ...
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### Propositional S5: is there a consistent set requiring continuously many worlds?

A recent question asked whether in systems of modal propositional logic having the "finite model property" there are consistent sets of sentences that were not satisfied by a finite model. @Carl ...
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### Propositional modal logic: infinite models required in systems with finite model property?

A system of propositional modal logic has the "finite model property" if any consistent sentence is satisfiable at a model with finitely many possible worlds. Some systems have this property and ...
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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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### Explanation of states, worlds and models?

Can someone explain to me how the concepts of states, models and worlds work together in Kripke semantics? I've been trying to piece together how the parts work are linked together but cannot figure ...
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### Question concerning satisfiability in a certain Kripke model

My question concerns the exercise on p.77 of Boolos, Logic of Provability: True or false: if $A$ is satisfiable in some finite transitive and irreflexive [FIT] model and contains at most one ...
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308 views

### What is the difference between First-Order Structures and Kripke Structures?

In the SEP article on Model Theory by Wilfrid Hodges (here), he writes: Particular kinds of model theory use particular kinds of structure; for example mathematical model theory tends to use so-...
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### A question on intuitionistc propositional logic

Prove that: Two finite rooted frames are isomorphic iff they validate the same formulas. (This is an exercise in the book "Modal Logic" by A.Chagrov and M.Zakharyaschev)