A System for Strict Implication

概要

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It is well known that in classical logic, there exist some kinds of provable formulas such as β⊃.α⊃α, β⊃.α∨〜α, α・〜α.⊃β, α⊃.β⊃α, α⊃.β⊃α・β, etc. Although the provability of these formulas never diminishes the value of classical logic, we are obliged to take these formulas as including somewhat redundant or, at least, unimportant implication. Some attempts have been made to formulate a system being free from the provability of these formulas. But they are still unsatisfactory in some ways. Therefore, as a new attempt, we should like to propose a decidable system which contains the classical sentential calculus and is free from the above mentioned provability.
科学基礎論学会の論文
1964-02-29