## Regaining Cut Admissibility in Deduction Modulo using Abstract Completion (2009)

Citations: | 2 - 1 self |

### BibTeX

@MISC{Burel09regainingcut,

author = {Guillaume Burel and Claude Kirchner},

title = { Regaining Cut Admissibility in Deduction Modulo using Abstract Completion},

year = {2009}

}

### OpenURL

### Abstract

Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore. We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system. Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth-Bendix completion in a non-trivial way, using the framework of abstract canonical systems. These