“contraction”的概念、定义、翻译、参考文献-科学参考

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.

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.
随便看	marginal check marginal conditions for optimality marginal cost marginal cost of abatement marginal cost pricing marginal distribution marginal effect marginal efficiency of investment marginal firm marginal homogeneity marginalization marginal land marginal physical product marginal private benefit marginal private cost marginal product marginal propensity to consume marginal propensity to import marginal propensity to save marginal rate of substitution marginal rate of technical substitution marginal rate of transformation marginal revenue marginal revenue product marginal sea