“residuum”的概念、定义、翻译、参考文献-科学参考

residuum

Logic

In a deductive system $L$ with a binary connective $\circ$ , describes the binary connective $\to$ satisfying the following scheme for all $φ$ , $ψ$ , and $ξ$ :
$φ \circ ψ ⊢_{L} ξ$ iff $φ ⊢_{L} ψ \to ξ$
In classical logic, for example, material implication is the residuum (or residual) of conjunction. Likewise, in relevant logic, relevant implication serves as the residuum for the binary connective of fusion. The notion is especially important in the case of fuzzy logic, in which distinct species of fuzzy implication are defined as the residua of distinct triangular norms.

单词	residuum
释义	residuum Logic In a deductive system $L$ with a binary connective $\circ$ , describes the binary connective $\to$ satisfying the following scheme for all $φ$ , $ψ$ , and $ξ$ : $φ \circ ψ ⊢_{L} ξ$ iff $φ ⊢_{L} ψ \to ξ$ In classical logic, for example, material implication is the residuum (or residual) of conjunction. Likewise, in relevant logic, relevant implication serves as the residuum for the binary connective of fusion. The notion is especially important in the case of fuzzy logic, in which distinct species of fuzzy implication are defined as the residua of distinct triangular norms.
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