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Simple free starautonomous categories and full coherence
, 2005
"... This paper gives a simple presentation of the free starautonomous category over a category, based on EilenbergKellyMacLane graphs and Trimble rewiring, for full coherence. ..."
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Cited by 12 (0 self)
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This paper gives a simple presentation of the free starautonomous category over a category, based on EilenbergKellyMacLane graphs and Trimble rewiring, for full coherence.
Exhausting Strategies, Joker Games and Full Completeness for IMLL with Unit
 In Proc. 8th Conf. CTCS'99. ENTCS 29
, 1999
"... We present a game description of free symmetric monoidal closed categories, which can also be viewed as a fully complete model for the Intuitionistic Multiplicative Linear Logic with the tensor unit. We model the unit by a distinguished onemove game called Joker. Special rules apply to the joker mo ..."
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Cited by 11 (6 self)
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We present a game description of free symmetric monoidal closed categories, which can also be viewed as a fully complete model for the Intuitionistic Multiplicative Linear Logic with the tensor unit. We model the unit by a distinguished onemove game called Joker. Special rules apply to the joker move. Proofs are modelled by what we call conditionally exhausting strategies, which are deterministic and total only at positions where no joker move exists in the immediate neighbourhood, and satisfy a kind of reachability condition called Pexhaustion. We use the model to give an analysis of a counting problem in free autonomous categories which generalises the Triple Unit Problem. 1 Introduction We aim to construct a fully complete game model for IMLL with unit, the intuitionistic multiplicative (\Omega ; (;?)fragment of Linear Logic (we write ? for the tensor unit). The notion of full completeness [2] is best formulated in terms of a categorical model of the logic, in which formulas (or...
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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Cited by 10 (4 self)
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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
Coherence of the Double Involution on * Autonomous Categories. Theory and Applications of Category Theory
, 2005
"... Abstract. We show that any free ∗autonomous category is equivalent (in a strict sense) to a free ∗autonomous category in which the doubleinvolution (−) ∗∗ is the identity functor and the canonical isomorphism A ≃ A∗ ∗ is an identity arrow for all A. 1. ..."
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Cited by 4 (0 self)
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Abstract. We show that any free ∗autonomous category is equivalent (in a strict sense) to a free ∗autonomous category in which the doubleinvolution (−) ∗∗ is the identity functor and the canonical isomorphism A ≃ A∗ ∗ is an identity arrow for all A. 1.
Simple multiplicative proof nets with units
, 2005
"... Abstract. This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units during normalisation. Composition ..."
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Cited by 4 (1 self)
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Abstract. This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units during normalisation. Composition
Normalization Bounds in Rudimentary Linear Lambda Calculus
"... Surprisingly we show that in rudimentary intuitionistic linear lambda calculus there are no linear bounds for normalizing terms under substitutions when commuting conversions are considered. We show that such a bound exists if we only count reductions or consider evaluation to values of closed term ..."
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Surprisingly we show that in rudimentary intuitionistic linear lambda calculus there are no linear bounds for normalizing terms under substitutions when commuting conversions are considered. We show that such a bound exists if we only count reductions or consider evaluation to values of closed terms.