Zero-one laws for modal logic
It is shown that a 0-1 law holds for propositional modal logic, both for structure validity and frame validity. The problem of deciding whether a formula is almost-surely frame valid is \(\text{P}^{\text{NP}}\), the corresponding decision problem for frame validity is hard for deterministic exponential time. The relationship to 0-1 laws for fragments of second-order logic is discussed in detail.
scientific article; zbMATH DE number 683706
scientific article