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A Judgmental Reconstruction of Modal Logic
 Mathematical Structures in Computer Science
, 1999
"... this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deduction for ..."
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Cited by 160 (38 self)
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this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deduction for intuitionistic modal logic which does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic [FM97] and find that it is already contained in modal logic, using the decomposition of the lax modality fl A as
A short proof of the Strong Normalization of Classical Natural Deduction with Disjunction
 Journal of symbolic Logic
, 2003
"... We give a direct, purely arithmetical and elementary proof of the strong normalization of the cutelimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction. 1 ..."
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Cited by 23 (14 self)
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We give a direct, purely arithmetical and elementary proof of the strong normalization of the cutelimination procedure for full (i.e. in presence of all the usual connectives) classical natural deduction. 1
Confluency property of the callbyvalue λµ ∧∨  calculus
 Computational Logic and Applications CLA’05. Discrete Mathematics and Theoretical Computer Science proc
, 2006
"... LAMA Équipe de logique, Université de Savoie, F73376 Le Bourget du Lac, France In this paper, we introduce the λµ ∧ ∨ callbyvalue calculus and we give a proof of the ChurchRosser property of this system. This proof is an adaptation of that of Andou (2003) which uses an extended parallel reduct ..."
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Cited by 3 (0 self)
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LAMA Équipe de logique, Université de Savoie, F73376 Le Bourget du Lac, France In this paper, we introduce the λµ ∧ ∨ callbyvalue calculus and we give a proof of the ChurchRosser property of this system. This proof is an adaptation of that of Andou (2003) which uses an extended parallel reduction method and complete development. Keywords: Callbyvalue, ChurchRosser, Propositional classical logic, Parallel reduction, Complete development 1
Some properties of the λµ ∧ ∨calculus Karim NOUR & Khelifa SABER
"... In this paper, we present the λµ ∧ ∨calculus which at the typed level corresponds to the full classical propositional natural deduction system. ChurchRosser property of this system is proved using the standardization and the finiteness developments theorem. We define also the leftmost reduction an ..."
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In this paper, we present the λµ ∧ ∨calculus which at the typed level corresponds to the full classical propositional natural deduction system. ChurchRosser property of this system is proved using the standardization and the finiteness developments theorem. We define also the leftmost reduction and prove that it is a winning strategy. 1