A first course in fuzzy logic
A note on a deductive scheme of Dummett in classical and fuzzy logics
Fuzzy Sets and Systems
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By means of a syntactic concept of self-contradiction, the aristotelian principles of non-contradiction and excluded-middle are posed in some very simple algebraic structures. Once linked with an algebraic representation of the relation If/then, such framework allows to represent both principles, and to prove that there is always the smallest relation for which they do hold. Finally, in agreement with the semantics of the relation If/then, the principles are stated with fuzzy sets, and some progress is reached in this case for what concerns the verification of the two principles.