A Contribution to Automated-oriented Reasoning about Permutability of Sequent Calculi Rules

Tatjana Lutovac, James Harland

Many important results in proof theory for sequent calculus (cut-elimination, completeness and other properties of search strategies, etc) are proved using permutations of sequent rules. The focus of this paper is on the development of systematic and automated-oriented techniques for the analysis of permutability in some sequent calculi. A representation of sequent calculi rules is discussed, which involves greater precision than previous approaches, and allows for correspondingly more precise and more general treatment of permutations. We define necessary and sufficient conditions for the permutation of sequence rules. These conditions are specified as constraints between the multisets that constitute different parts of the sequent rules. The authors extend their previous work in this direction to include some special cases of permutations.