On Sets of Premises

Abstract

Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with the same premises and the same conclusions become equal. In terms of categorial proof theory, this is a consequence of a simple fact concerning adjunction with a full and faithful functor applied to the adjunction between the diagonal functor and the product biendofunctor, which corresponds to the conjunction connective.