# 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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### Necessity and sufficiency on dead end worlds in Kripke's model

Suppose we are evaluating $\square p$, $\diamondsuit$p, $\square\square$p, $\diamondsuit\diamondsuit$p, $\square$$\diamondsuitp, \diamondsuit$$\square$p on a dead end world (the world that can't ...
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### Semantic explanation for converting intuitionistic logic into classical logic by adding LEM as an axiom

I have a question about converting intuitionistic logic (IL) into classical logic (CL) by adding LEM as an axiom. IL is usually understood as a logic without LEM. $$\textrm{LEM}:=A\vee\neg A.$$ In ...
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### Accessibility relation in non-classical logics: hereditary or not?

Recently, I am reading course materials on intuitionistic and modal logics. I have two questions about the notion of accessibility relation in Kripke semantics for intuitionistic and modal logics. ...
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### Proofing transitivity of simulation relation in Kripke structures

I would like to proof transitivity of simulation in Kripke Structures. Proof Sketch: Let A, B, C be Kripke Structures, with A=(Sa,S0a,Ra,AP,La) B=(Sb,S0b,Rb,AP,Lb) C=(Sc,S0c,Rc,AP,Lc) H ⊆ S × S′ ...
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### What is the difference between turnstile and implication in Kripke frames? [duplicate]

First, let me clarify the notations. 1) $\mathfrak{F} =(X,R)$ is a Kripke frame. 2) $v$ is a valuation from the sets of variables to the powerset of $X$, extended to formulas in the usual way. 3) ...
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### what does the “fixed point” in fixpoint algorithms refer to?

I was reading the following powerpoint here to remember something I studied a long time ago. http://www.cs.cmu.edu/~emc/15-820A/reading/lecture_1.pdf the 12th slide is labeled fixpoint algorithms, ...
174 views

### Proving the non-derivability of formula using the of the kripke model

I try proving the non-derivability of $(p\to q) \to \lnot p \lor q$, using the of the kripke model. I tried using different combinations of $Wi$, but I get fail.
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