Volume 1, Issue 4 (2022)                   jpt 2022, 1(4): 0-0 | Back to browse issues page

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Mirsanei S A. Proof theory of Provability Logic. jpt. 2022; 1 (4)
URL: http://jpt.modares.ac.ir/article-34-57996-en.html
PhD student in Philosophy Logic, Department of Philosophy, Wisdom and Logic, Faculty of Humanities, Tarbiat Modares University, Tehran , sa.mir@modares.ac.ir
Abstract:   (70 Views)
Discovering the differences between the various systems of modal logics was one of the advantages of inventing Kripke semantics. One of the most obvious examples is the interpretation of the necessity of provability in provability logic, and according to Boolos in The Logic of Provability, by discovering this logic, we can say that the understanding of new issues in the field of argument was opened. In this paper, with a formal approach and with a descriptive-analytical and comparative method, the axiomatic propositional systems of the GL, Grz and H, and their possible world semantics based on Kripke semantics are studied, as well as the sequent calculus of GL (in Peano arithmetic) and GLS (in the standard model) were introduced, and finally, the meta-theorems of soundness, consistency and completeness of the GL were interpreted and proved.
     
Article Type: Original Research | Subject: Logic and Philosophy of Logic (Modern)
Received: 2021/12/18 | Accepted: 2021/12/27 | Published: 2022/01/4

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