“contraction”的概念、定义、翻译、参考文献-科学参考

contraction

Logic

单词	contraction
释义	contraction Logic 1. In proof theory, a structural rule according to which one may elide a redundant instance of a formula $φ$ from a cedent $Γ$ whenever two or more instances of $φ$ appear in $Γ$ . More formally, this is represented in left and right versions: $\frac{Γ, φ, φ \Rightarrow Δ}{Γ, φ \Rightarrow Δ} L-Con \frac{Γ \Rightarrow Δ, φ, φ}{Γ \Rightarrow Δ, φ} R-Con$ 2. When $\to$ is a conditional connective, the classically valid inference $\frac{φ \to (φ \to ψ)}{φ \to ψ}$ Contraction in this form plays an especially important role in the formulation of Curry’s paradox, which has motivated support for contraction-free logics. The axiomatic representation of the foregoing inference frequently appears as: • $(φ \to (φ \to ψ)) \to (φ \to ψ)$ 3. In belief revision, an operation that removes a sentence from a belief set.
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