deduction theorem

English

deduction theorem (plural deduction theorems)

(logic) A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form ${\\displaystyle P,A\\vdash C}$ to an inference of the form ${\\displaystyle P\\vdash A\\rightarrow C}$ or vice versa, where ${\\displaystyle \\vdash }$ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory.
The deduction theorem reveals the relationship between logical entailment and material implication: it allows to one to "pack" or "record" an inference into a tautology, and conversely, to "unpack" or "play back" a tautology as an inference process.

单词	deduction theorem
释义	deduction theorem English Noun deduction theorem (plural deduction theorems) (logic) A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form ${\\displaystyle P,A\\vdash C}$ to an inference of the form ${\\displaystyle P\\vdash A\\rightarrow C}$ or vice versa, where ${\\displaystyle \\vdash }$ is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory. The deduction theorem reveals the relationship between logical entailment and material implication: it allows to one to "pack" or "record" an inference into a tautology, and conversely, to "unpack" or "play back" a tautology as an inference process. See also conditional proof
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