Varieties of linear calculi

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

Authors
Sara Negri
University of Helsinki
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.
Keywords general rules  inversion principle  linear logic
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1021264102972
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,330
Through your library

References found in this work BETA

Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.

View all 11 references / Add more references

Citations of this work BETA

On Inversion Principles.Enrico Moriconi & Laura Tesconi - 2008 - History and Philosophy of Logic 29 (2):103-113.
Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
82 ( #106,592 of 2,286,097 )

Recent downloads (6 months)
1 ( #835,155 of 2,286,097 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature