Abstract

Intuitionistic Propositional LogicIntuitionistic propositional logic is proved to be an infinitely many valued logicMany valued logics by Gödel Publications 1929–1936, Oxford University Press, pp 222–225, 1932), and it is proved by Jaśkowski Jaśkowski, S. to be a countably many valued logicMany valued logics. In this paper, we provide alternative proofs for these theorems by using models of Kripke :1–14, 1959). Gödel’s proof gave rise to an intermediate propositional logic, that is known nowadays as Gödel or the Gödel-Dummett LogicGödel-Dummet Logic, and is studied by fuzzy logicians as well. We also provide some results on the inter-definability of propositional connectivesInter-definability of propositional connectives in this logic.