Archive for Mathematical Logic 42 (3):221-243 (2003)

Valentin Goranko
Stockholm University
We study the modal logic M L r of the countable random frame, which is contained in and `approximates' the modal logic of almost sure frame validity, i.e. the logic of those modal principles which are valid with asymptotic probability 1 in a randomly chosen finite frame. We give a sound and complete axiomatization of M L r and show that it is not finitely axiomatizable. Then we describe the finite frames of that logic and show that it has the finite frame property and its satisfiability problem is in EXPTIME. All these results easily extend to temporal and other multi-modal logics. Finally, we show that there are modal formulas which are almost surely valid in the finite, yet fail in the countable random frame, and hence do not follow from the extension axioms. Therefore the analog of Fagin's transfer theorem for almost sure validity in first-order logic fails for modal logic
Keywords modal logic  countable random frame  zero-one laws  complete axiomatization  almost sure frame validity
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DOI 10.1007/s001530100135
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Zero-One Laws for Modal Logic.Jospeh Halpern & Bruce Kapron - 1994 - Annals of Pure and Applied Logic 69 (2-3):157-193.

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