We present a sequent calculus for the modal logic S4, and by building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings to axioms and modal rules) 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 (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.
A modal view of linear logic
MASINI, Andrea
1994-01-01
Abstract
We present a sequent calculus for the modal logic S4, and by building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings to axioms and modal rules) 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 (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.
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