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Gentzen’s rules of natural deduction define the basic inference patterns which govern the use of logical constants within the logical system of natural deduction. In general, these rules are considered to represent a model that significantly approximates the actual use of counterparts of logical constants by competent speakers in everyday communication. Despite the fact that Gentzen’s system is assumed...
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 non-strictly positive inductive definitions.It covers second-order universal quantification and also the extension of the logic with fixed points of non-strictly positive operators, which appears to be a new...
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