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

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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DOI 10.1007/BF01053259
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References found in this work BETA

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.
On the Proof Theory of the Modal Logic Grz.M. Borga & P. Gentilini - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (10-12):145-148.
On the Proof Theory of the Modal Logic Grz.M. Borga & P. Gentilini - 1986 - Mathematical Logic Quarterly 32 (10‐12):145-148.

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Citations of this work BETA

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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