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Fundam. Prikl. Mat., 1997, Volume 3, Issue 4, Pages 1173–1197 (Mi fpm269)  

This article is cited in 1 scientific paper (total in 1 paper)

Provability logic with operations over proofs

T. L. Sidon

M. V. Lomonosov Moscow State University

Abstract: We present a natural axiomatization for propositional logic with modal operator for formal provability (Solovay, [5]) and labeled modalities for individual proofs with operations over them (Artemov, [2]). For this purpose the language is extended by two new operations. The obtained system $\mathcal{MLP}$ naturally includes both Solovay's provability logic GL and Artemov's operational modal logic $\mathcal{LP}$. All finite extensions of the basic system $\mathcal{MLP}_{0}$ are proved to be decidable and arithmetically complete. It is shown that $\mathcal{LP}$ realizes all operations over proofs admitting description in the modal propositional language.

Full text: PDF file (1066 kB)

Bibliographic databases:
UDC: 510.6
Received: 01.01.1997

Citation: T. L. Sidon, “Provability logic with operations over proofs”, Fundam. Prikl. Mat., 3:4 (1997), 1173–1197

Citation in format AMSBIB
\Bibitem{Sid97}
\by T.~L.~Sidon
\paper Provability logic with operations over proofs
\jour Fundam. Prikl. Mat.
\yr 1997
\vol 3
\issue 4
\pages 1173--1197
\mathnet{http://mi.mathnet.ru/fpm269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794509}
\zmath{https://zbmath.org/?q=an:0929.03058}


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    This publication is cited in the following articles:
    1. R. È. Yavorskii, “On Prenex Fragment of Provability Logic with Quantifiers on Proofs”, Proc. Steklov Inst. Math., 242 (2003), 112–124  mathnet  mathscinet  zmath
  • Фундаментальная и прикладная математика
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