Varieties of linear calculi

Journal of Philosophical Logic 31 (6):569-590 (2002)

Abstract

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations.

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References found in this work

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
Sequent Calculus in Natural Deduction Style.Sara Negri & Jan von Plato - 2001 - Journal of Symbolic Logic 66 (4):1803-1816.

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Citations of this work

On Inversion Principles.Enrico Moriconi & Laura Tesconi - 2008 - History and Philosophy of Logic 29 (2):103-113.
Necessity of Thought.Cesare Cozzo - 2015 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Springer. pp. 101-20.
Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
A Normalizing System of Natural Deduction for Intuitionistic Linear Logic.Sara Negri - 2002 - Archive for Mathematical Logic 41 (8):789-810.

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