Non-commutative first-order sequent calculus

Authors:
Makoto Tatsuta
Affiliations:
National Institute of Informatics, Tokyo, Japan
Venue:
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Year:
2009

Citing 2
Cited 0

Linear logic

Theoretical Computer Science
Positive arithmetic without exchange is a subclassical logic

APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems

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Abstract

This paper investigates a non-commutative first-order sequent calculus NCLK. For that, this paper extends a noncommutative positive fragment to a full first-order sequent calculus LK- having antecedent-grouping and no right exchange rule. This paper shows (1) NCLK is equivalent to LJ, (2) NCLK with the exchange rule is equivalent to LK, (3) LK- is equivalent to LJ, and (4) translations between LK- and NCLK.