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A modal view of linear logic

Published online by Cambridge University Press:  12 March 2014

Simone Martini  and
Andrea Masini
Simone Martini
Affiliation:
Dipartimento di Informatica, Università di Pisa, Corso Italia, 40, 1-56125 Pisa, Italy, E-mail: martini@di.unipi.it
Andrea Masini
Affiliation:
Dipartimento di Informatica, Università di Pisa, Corso Italia, 40, 1-56125 Pisa, Italy, E-mail: masini@di.unipi.it
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Abstract

We present a sequent calculus for the modal logic S4, and building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings into axioms and modal rules) we show how S4 can easily be translated into full prepositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities (exponentials) 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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 3 , September 1994 , pp. 888 - 899
Copyright
Copyright © Association for Symbolic Logic 1994

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