FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 4, PAGES 1173-1197
T. L. Sidon
Abstract
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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.
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