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Dual Intuitionistic Linear Logic

Andrew Barber

Open publisher page 172 citations

Abstract

We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to reflect the motivation of exponentials as translations of intuitionistic types, and provide it with a term calculus, proving associated standard type-theoretic results. We give a sound and complete categorical semantics for the type-system, and consider the relationship of the new type-theory to the more familiar presentation found for example in [4].

About this research paper

What this paper is about

We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to reflect the motivation of exponentials as translations of intuitionistic types, and provide it with a term calculus, proving associated standard type-theoretic results. We give a sound and complete categorical semantics for the type-system, and consider the relationship of the new type-theory to the more familiar presentation found for example in [4].

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OpenAlex reports 172 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a new intuitionistic linear logic, Dual Intuitionistic Linear Logic, designed to reflect the motivation of exponentials as translations of intuitionistic types, and provide it with a term calculus, proving associated standard type-theoretic results. We give a sound and complete categorical semantics for the type-system, and consider the relationship of the new type-theory to the more familiar presentation found for example in [4].

Key concepts: Linear logic, Intuitionistic logic, Type theory, Mathematics, Categorical variable, Minimal logic, Calculus (dental), Algebra over a field

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