A modal view of linear logic

Journal of Symbolic Logic 59 (3):888-899 (1994)
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We present a sequent calculus for the modal logic S4, and building on some relevant features of this system we show how S4 can easily be translated into full propositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities only in correspondence with S4 modalities. We discuss the complexity of the decision problem for several classes of linear formulas naturally arising from the proposed translations.



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Citations of this work

A linear approach to modal proof theory.Harold Schellinx - 1996 - In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer Academic Publishers. pp. 33.
Linear Logic and Lukasiewicz ℵ0- Valued Logic: A Logico-Algebraic Study.Jayanta Sen & M. K. Chakraborty - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):313-329.

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Foundations of Mathematical Logic.William Craig - 1963 - Journal of Symbolic Logic 45 (2):377-378.
Modal logic, the Lewis-modal systems.J. Jay Zeman - 1973 - Revue Philosophique de la France Et de l'Etranger 163:479-479.
Linearizing intuitionistic implication.Patrick Lincoln, Andre Scedrov & Natarajan Shankar - 1993 - Annals of Pure and Applied Logic 60 (2):151-177.
Modal Logics.Robert Feys & J. Dopp - 1965 - Journal of Symbolic Logic 34 (3):501-502.

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