## Theorem Proving Modulo

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### Download Links

- [www.loria.fr]
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- [www.loria.fr]
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### Other Repositories/Bibliography

Venue: | Journal of Automated Reasoning |

Citations: | 75 - 14 self |

### BibTeX

@ARTICLE{Dowek_theoremproving,

author = {Gilles Dowek and Thérèse Hardin and Claude Kirchner},

title = {Theorem Proving Modulo},

journal = {Journal of Automated Reasoning},

year = {},

pages = {2003}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof theoretic account of the combination of computations and deductions. The congruence on propositions is handled via rewrite rules and equational axioms. Rewrite rules apply to terms and also directly to atomic propositions. The second contribution is to give a complete proof search method, called Extended Narrowing and Resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo. An important application is that higher-order logic can be presented as a theory modulo. Applying the Extended Narrowing and Resolution method to this presentation of higher-order logic subsumes full higher-order resolution.