Computational isomorphisms in classical logic

Authors:
Vincent Danos;Jean-Baptiste Joinet;Harold Schellinx
Affiliations:
Équipe de Logique Mathématique, Université Paris VII, France;Équipe de Logique Mathématique, Université Paris VII, France;Mathematisch Instituut, Universiteit Utrecht, Netherlands
Venue:
Theoretical Computer Science - Linear logic
Year:
2003

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Abstract

All standard 'linear' boolean equations are shown to be computationally realized within a suitable classical sequent calculus LKηp. Specifically, LKηp can be equipped with a cut-elimination compatible equivalence on derivations based upon reversibility properties of logical rules. So that any pair of derivations, without structural rules, of F → G and G → F, where F, G are first-order formulas 'without any qualities', defines a computational isomorphism.