Rosser Provability and Normal Modal Logics

Studia Logica 108 (3):597-617 (2020)
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Abstract

In this paper, we investigate Rosser provability predicates whose provability logics are normal modal logics. First, we prove that there exists a Rosser provability predicate whose provability logic is exactly the normal modal logic \. Secondly, we introduce a new normal modal logic \ which is a proper extension of \, and prove that there exists a Rosser provability predicate whose provability logic includes \.

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Citations of this work

Arithmetical completeness theorems for monotonic modal logics.Haruka Kogure & Taishi Kurahashi - 2023 - Annals of Pure and Applied Logic 174 (7):103271.

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References found in this work

A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
A New Introduction to Modal Logic.G. E. Hughes & M. J. Cresswell - 1996 - Studia Logica 62 (3):439-441.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.

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