Syntactical results on the arithmetical completeness of modal logic

Studia Logica 52 (4):549 - 564 (1993)
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Abstract

In this paper the PA-completeness of modal logic is studied by syntactical and constructive methods. The main results are theorems on the structure of the PA-proofs of suitable arithmetical interpretationsS of a modal sequentS, which allow the transformation of PA-proofs ofS into proof-trees similar to modal proof-trees. As an application of such theorems, a proof of Solovay's theorem on arithmetical completeness of the modal system G is presented for the class of modal sequents of Boolean combinations of formulas of the form p i,m i=0, 1, 2, ... The paper is the preliminary step for a forthcoming global syntactical resolution of the PA-completeness problem for modal logic.

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Citations of this work

Provability Logic in the Gentzen Formulation of Arithmetic.Paolo Gentilini & P. Gentilini - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):535-550.

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References found in this work

Proof Theory.Gaisi Takeuti - 1975 - Elsevier.
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
The Modal Logic of Provability. The Sequential Approach.Giovanni Sambin & Silvio Valentini - 1982 - Journal of Philosophical Logic 11 (3):311 - 342.
Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.

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