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  1. Natural deduction with general elimination rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
    The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, no inactive weakening (...)
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  • A Problem of Normal Form in Natural Deduction.Jan von Plato - 2000 - Mathematical Logic Quarterly 46 (1):121-124.
    Recently Ekman gave a derivation in natural deduction such that it either contains a substantial redundant part or else is not normal. It is shown that this problem is caused by a non-normality inherent in the usual modus ponens rule.
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