From Intuitionism to Many-Valued Logics Through Kripke Models

In Mojtaba Mojtahedi, Shahid Rahman & Mohammad Saleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 339-348 (2021)
Download Edit this record How to cite View on PhilPapers
Abstract
Intuitionistic Propositional Logic is proved to be an infinitely many valued logic by Gödel (Kurt Gödel collected works (Volume I) Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski (Actes du Congrés International de Philosophie Scientifique, VI. Philosophie des Mathématiques, Actualités Scientifiques et Industrielles 393:58–61, 1936) to be a countably many valued logic. In this paper, we provide alternative proofs for these theorems by using models of Kripke (J Symbol Logic 24(1):1–14, 1959). Gödel’s proof gave rise to an intermediate propositional logic (between intuitionistic and classical), that is known nowadays as Gödel or the Gödel-Dummett Logic, and is studied by fuzzy logicians as well. We also provide some results on the inter-definability of propositional connectives in this logic.
Categories
(categorize this paper)
PhilPapers/Archive ID
SALGIP-2
Upload history
First archival date: 2021-02-21
Latest version: 3 (2021-02-21)
View other versions
Added to PP index
2021-02-21

Total views
11 ( #57,732 of 56,906 )

Recent downloads (6 months)
11 ( #46,961 of 56,906 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.