Abstract

Given a class $\mathcal{𝒞}$ of finite Kripke frames, we consider the uniform distribution on the frames from $\mathcal{𝒞}$ with $n$ states. A formula is almost surely valid in $\mathcal{𝒞}$ if the probability that it is valid in a random $\mathcal{𝒞}$-frame with $n$ states tends to $1$ as $n$ tends to infinity. The formulas that are almost surely valid in $\mathcal{𝒞}$ form a normal modal logic.

We find complete and sound axiomatizations for the logics of almost-sure validities in the classes of finite frames defined by the logics $KD5$, $KD45$, $K5B$, $S5$, $Grz.3$, and $GL.3$.

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Mathematical Subject Classification

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