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Classical linear logic of implications
 In Proc. Computer Science Logic (CSL'02), Springer Lecture Notes in Comp. Sci. 2471
, 2002
"... Abstract. We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear andlinear implications as the basic constructs, andthis design choice allows a technica ..."
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Abstract. We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s system for the intuitionistic case. The calculus has the nonlinear andlinear implications as the basic constructs, andthis design choice allows a technically managable axiomatization without commuting conversions. Despite this simplicity, the calculus is shown to be sound andcomplete for categorytheoretic models given by ∗autonomous categories with linear exponential comonads. 1
A terminating and confluent linear lambda calculus
 PROC. OF 17TH INT. CONFERENCE RTA 2006, VOLUME 4098 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... We present a rewriting system for the linear lambda calculus corresponding to the {!, ⊸}fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and ChurchRosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the eq ..."
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Cited by 8 (0 self)
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We present a rewriting system for the linear lambda calculus corresponding to the {!, ⊸}fragment of intuitionistic linear logic. This rewriting system is shown to be strongly normalizing, and ChurchRosser modulo the trivial commuting conversion. Thus it provides a simple decision method for the equational theory of the linear lambda calculus. As an application we prove the strong normalization of the simply typed computational lambda calculus by giving a reductionpreserving translation into the linear lambda calculus.
f!;(g is Full in f!; (g
"... We show that the f!;(gfragment of Intuitionistic Linear Logic is full in the f!; (gfragment, both formulated as linear lambda calculi. The proof is a mild extension of our previous technique used for showing the fullness of Girard's translation from Intuitionistic Logic into Intuitionistic ..."
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We show that the f!;(gfragment of Intuitionistic Linear Logic is full in the f!; (gfragment, both formulated as linear lambda calculi. The proof is a mild extension of our previous technique used for showing the fullness of Girard's translation from Intuitionistic Logic into Intuitionistic Linear Logic, and makes use of doubleparameterized logical predicates.
Under consideration for publication in Math. Struct. in Comp. Science Classical Linear Logic of Implications
, 2003
"... We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s dualcontext system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a te ..."
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We give a simple term calculus for the multiplicative exponential fragment of Classical Linear Logic, by extending Barber and Plotkin’s dualcontext system for the intuitionistic case. The calculus has the nonlinear and linear implications as the basic constructs, and this design choice allows a technically manageable axiomatization without commuting conversions. Despite this simplicity, the calculus is shown to be sound and complete for categorytheoretic models given by ∗autonomous categories with linear exponential comonads. 1.