Zero-one laws for modal logic

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Annals of Pure and Applied Logic 69 (2-3):157-193 (1994)
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Abstract

We show that a 0–1 law holds for propositional modal logic, both for structure validity and frame validity. In the case of structure validity, the result follows easily from the well-known 0–1 law for first-order logic. However, our proof gives considerably more information. It leads to an elegant axiomatization for almost-sure structure validity and to sharper complexity bounds. Since frame validity can be reduced to a Π11 formula, the 0–1 law for frame validity helps delineate when 0–1 laws exist for second-order logics.

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10.1016/0168-0072(94)90084-1

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Citations of this work

The modal logic of the countable random frame.Valentin Goranko & Bruce Kapron - 2003 - Archive for Mathematical Logic 42 (3):221-243.

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References found in this work

On Some Completeness Theorems in Modal Logic.D. Makinson - 1966 - Mathematical Logic Quarterly 12 (1):379-384.
Probabilities on finite models.Ronald Fagin - 1976 - Journal of Symbolic Logic 41 (1):50-58.
Monadic generalized spectra.Ronald Fagin - 1975 - Mathematical Logic Quarterly 21 (1):89-96.

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