Intuitionistic logic

FUZZY LOGIC

Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014

The last postulate of Definition 3.24 is the most controversial one. In order to preserve a continuum of degrees of truth, we should restrict the notion of logical equivalence. In intuitive descriptions, fuzzy logic is often characterized as arising from the rejection of the law of excluded middle: the assertion AV A. Unfortunately, rejecting this law is not sufficient to avoid collapse to just two truth values. Intuitionistic logic rejects the law of excluded middle, but the formal system of Definition 3.24 still collapses when logical equivalence means intuitionistic equivalence. Of course, collapse

Bi-intuitionistic implication structures

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Journal Information

Published in Journal of Applied Non-Classical Logics, 2018

Daniel Skurt

Based on the above definitions, Koslow was able to prove two soundness and completeness results. If an implication structure is classical then the theses of this structure are exactly the theorems of classical logic, and if it is non-classical then the theses are exactly the theorems of intuitionistic logic, if the required operators exist.

Intuitionistic logic

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FUZZY LOGIC

Bi-intuitionistic implication structures