A Remark on the Intersection of Tow Logics

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Abstract
The intuitionistic logic LJ and Curry’s LD (cf. [1], [2]) are logics stronger than Johansson’s minimal logic LM (cf. [3]) by the axiom schemes ⋏→x and y ∨ (y→⋏), respectively. However, LM can not be taken literally as the intersection of these two logics LJ and LD, which is stronger than LM by the axiom scheme (⋏ → x) VyV (y→⋏). In pointing out this situation, Prof. K. Ono suggested me to investigate the general feature of the intersection of any pair of logics. In this paper, I will show that the same situation occurs in general. I wish to express my thanks to Prof. K. Ono for his kind guidance.

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