Intuitionistic mathematics does not needex falso quodlibet

Topoi 13 (2):127-133 (1994)
Abstract
We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consistent set of premisses.
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References found in this work BETA
H. A. Lewis & Neil Tennant (1981). Natural Logic. Philosophical Quarterly 31 (125):376.
N. Tennant (1980). A Proof-Theoretic Approach to Entailment. Journal of Philosophical Logic 9 (2):185 - 209.

View all 7 references

Citations of this work BETA
Neil Tennant (2012). Cut for Core Logic. Review of Symbolic Logic 5 (3):450-479.
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