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Zero-one laws for modal logic

Jospeh Halpern & Bruce Kapron

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

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The modal logic of the countable random frame.Valentin Goranko & Bruce Kapron - 2003 - Archive for Mathematical Logic 42 (3):221-243.details 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 (...) Download Export citation Bookmark 1 citation
On the expressiveness of frame satisfiability and fragments of second-order logic.Thomas Eiter & Georg Gottlob - 1998 - Journal of Symbolic Logic 63 (1):73-82.details It was conjectured by Halpern and Kapron (Annals of Pure and Applied Logic, vol. 69, 1994) that frame satisfiability of propositional modal formulas is incomparable in expressive power to both Σ 1 1 (Ackermann) and Σ 1 1 (Bernays-Schonfinkel). We prove this conjecture. Our results imply that Σ 1 1 (Ackermann) and Σ 1 1 (Bernays-Schonfinkel) are incomparable in expressive power, already on finite graphs. Moreover, we show that on ordered finite graphs, i.e., finite graphs with a successor, Σ 1 (...) Download Export citation Bookmark

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