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An Introduction to Fuzzy Implications

2008; Springer Nature; Linguagem: Inglês

10.1007/978-3-540-69082-5_1

1860-0808

Michał Baczyński, Balasubramaniam Jayaram,

Advanced Algebra and Logic

The implication operator (→) plays a significant role in the classical two-valued logic. Firstly, from the classical implication one can obtain all other basic logical connectives of the binary logic, viz., the binary operators - and ( $\land$ ), or ( $\lor$ ) - and the unary negation operator (¬). Secondly, the implication operator holds the center stage in the inference mechanisms of any logic, like modus ponens, modus tollens, hypothetical syllogism in classical logic.