@MISC{Inference_.2classical, author = {The Inference}, title = {.2 Classical Logic}, year = {} }

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Abstract

Since hypotheses and their restrictions are critical for linear logic, we give here a formulation of natural deduction for intuitionistic logic with localized hypotheses, but not parameters. For this we need a notation for hypotheses which we call a context. Contexts \Gamma ::= \Delta j \Gamma; u:A Here, "\Delta" represents the empty context, and \Gamma; u:A adds hypothesis ` A labelled u to \Gamma. We assume that each label u occurs at most once in a context in order to avoid ambiguities. The main judgment can then be written as \Gamma ` A, where \Delta; u 1 :A 1 ; : : : ; un :An ` A stands for u 1 ` A 1 : : :<F43.12