A cut-like inference in a framework of explicit composition for various calculi of natural deduction
pp. 163-183
in: Gabriele Lolli, Marco Panza, Giorgio Venturi (eds), From logic to practice, Berlin, Springer, 2015Abstract
An explicit concatenation rule (EC) is proposed, obtained by generalizations and formalization of one of the most intuitive principle of abstract reasoning, which governs the composition of abstract derivations from the left and from the right at the same time, via the mediation of control clauses that occur in the position of the major premise. The sets of control clauses necessary to express various different calculi of natural deduction—standard natural deduction, natural deduction with general elimination rules, "bioriented" natural deduction and their variants—are considered, with a specific focus on a control clause for co-identity, a cut-like inference expressing the principle of linear substitution and on the effect of its addition to these calculi.