# Questions tagged [modal-logic]

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### Counterexample equivalent in relevant logic DL

On page 7 in the article referred to below an axiom $D9$ is stated as follows: $$A\to B\to.\lnot(A \& \lnot B)~\\ (\text{equivalently: } (A\to\lnot A)\to\lnot A)$$ How may one prove the alleged ...
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### Deduction theorem for the modal mu-calculus

Does the modal mu-calculus have a deduction theorem? If yes, how is it stated? Does it have the 'classical' form (i.e. as in classical propositional logic) or is it more involved?
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### Interpretations of modal logic where $\Box$ means "valid"

Consider the propositional modal language in one propositional letter, $p$. Recall that a pointed Kripke frame is a Kripke frame $(W,R)$ with a designated world $w_0\in W$, and a sentence is valid in ...
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### The provability logic of $I\Delta_0+\Omega_1$ and complexity theory

Almost 30 years ago, a number of folks in provability logic tried to show that GL (see for instance the excellent survey by Rineke Verbrugge here) is indeed the logic of $I\Delta_0+\Omega_1$ (in the ...
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### Sum and Product game

Two perfect logicians Steve and Pete, who have never met, before are imprisoned by an eccentric villain. "I have two positive integer numbers x and y" he says to them. "I will tell Steve the sum x+y, ...
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### Expressing a model transformation by using monads in the simply-typed lambda calculus

In https://link.springer.com/content/pdf/10.1007/s10670-019-00128-z.pdf , page 16, the following clause is given for a modal operator $\langle R_k \rangle$ (see definition 4.2 for the definition of a ...
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### Are buttons really enough to bound validities by S4.2?

Joel Hamkins recently claimed on twitter that buttons suffice to bound the validities of a potentialist system to the modal logic S4.2 (see here), and that switches are not necessary. We have been ...