Philosophical Thought
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Volume 1, Issue 4 (2021)
J Clin Care Skill 2021, 1(4): 313-339 |
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History
Received: 2021/12/18 | Accepted: 2021/12/27 | Published: 2022/02/5
Received: 2021/12/18 | Accepted: 2021/12/27 | Published: 2022/02/5
How to cite this article
Nabavi L, Mirsanei S. Propositional Provability Logics. J Clin Care Skill 2021; 1 (4) :313-339
URL: http://jpt.modares.ac.ir/article-6-57996-en.html
URL: http://jpt.modares.ac.ir/article-6-57996-en.html
1- Department of Philosophy, Faculty of Humanities, Tarbiat Modares University, Tehran, Iran
Abstract (4434 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 interpreting the necessity of provability in provability logic. 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. Finally, the meta-theorems of soundness, consistency, and completeness of the GL were interpreted and proved.
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