English Dictionary

linear logic

名詞

(logic) A logic in which two structural rules are missing from its sequent calculus: those for weakening and contraction; which has some extra logical connectives, so that it has both "additive" and "multiplicative" versions of the typical binary connectives and truth constants; and which has a pair of modal, "exponential" operators for resource management, to help make up for the loss of the two structural rules.

日本語の意味

線形論理（linear logic）は、順序付けられた論理体系において、弱化規則と収縮規則という2つの構造的規則が除外されている論理体系です。 / この体系は、従来の二項論理結合子や真理値定数に対して、加法的（additive）および乗法的（multiplicative）なバリエーションが存在し、加えて資源管理の補完として、モーダルな「指数」演算子のペアを導入している点が特徴です。

Researchers studied linear logic to understand how the absence of weakening and contraction restricts copying and discarding of resources.

研究者たちは、弱化と収縮という構造規則が存在しない論理を研究し、その規則の欠如が資源の複製や破棄をどのように制限するかを理解しようとした。

意味（1）

(logic) A logic in which two structural rules are missing from its sequent calculus: those for weakening and contraction; which has some extra logical connectives, so that it has both "additive" and "multiplicative" versions of the typical binary connectives and truth constants; and which has a pair of modal, "exponential" operators for resource management, to help make up for the loss of the two structural rules.

Gentzen also wrote down inference rules suitable for the intuitionistic propositional and predicate calculi. These rules lack the mirror symmetry of the classical case. But in the 1980s, this symmetry was restored by Girard’s invention of ‘linear logic’ [43].

linear logics （ plural ）