Computer Science and Information Systems 2013 Volume 10, Issue 3, Pages: 1185-1210
https://doi.org/10.2298/CSIS120820043L
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A contribution to automated-oriented reasoning about permutability of sequent calculi rules
Lutovac Tatjana (Faculty of Electrical Engineering, Department of Applied Mathematics, Belgrade)
Harland James (School of Computer Science and Information Technology, RMIT University GPO Box V, Melbourne, Australia)
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.
Keywords: Automated reasoning, permutation, sequent calculi, proof search, linear logic
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