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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
NonStrictly Positive FixedPoints for Classical Natural Deduction, accepted for publication in APAL
, 2004
"... Termination for classical natural deduction is difficult in the presence of commuting/permutative conversions for disjunction. An approach based on reducibility candidates is presented that uses nonstrictly positive inductive definitions. It covers secondorder universal quantification and also the ..."
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Cited by 4 (0 self)
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Termination for classical natural deduction is difficult in the presence of commuting/permutative conversions for disjunction. An approach based on reducibility candidates is presented that uses nonstrictly positive inductive definitions. It covers secondorder universal quantification and also the extension of the logic by fixedpoints of nonstrictly positive operators, which appears to be a new result. Finally, the relation to Parigot’s strictlypositive inductive definition of his set of reducibility candidates and to his notion of generalized reducibility candidates is explained. Key words: PACS:
Strong normalization of classical natural deduction with disjunctions
"... This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPStranslation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conju ..."
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This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPStranslation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves natural deduction can be embedded into natural deduction with general elimination rules, strictly preserving proof normalization.
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
Khelifa SABER
"... A semantics of realisability for the classical propositional natural deduction ..."
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A semantics of realisability for the classical propositional natural deduction
Karim NOUR and Khelifa SABER
, 905
"... A semantical proof of the strong normalization theorem for full propositional classical natural deduction ..."
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A semantical proof of the strong normalization theorem for full propositional classical natural deduction
Digital Object Identifier (DOI): 10.1007/s001530050314y
, 2004
"... A semantical proof of the strong normalization theorem for full propositional classical natural deduction ..."
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A semantical proof of the strong normalization theorem for full propositional classical natural deduction
Strong normalization results by translation
"... We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1 ..."
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We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1