Sequent Calculi with procedure calls

Mahfuza Farooque 1, 2 Stéphane Graham-Lengrand 1, 2
2 PARSIFAL - Proof search and reasoning with logic specifications
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : In this paper, we study 3 focussed sequent calculi that are based on Miller-Liang's LKF system for polarised classical logic, and integrate the possibility to call a decision procedure for some background theory T . The main sequent calculus out of the three is LK(T), in which we prove cut-elimination. Changing the polarities of literals and connectives does not change the provability of formulae, only the shape of proofs. In order to prove this, we introduce a second sequent calculus, LK+(T ) that extends LK(T) with a relaxed focussing discipline. We then prove completeness of LK(T) (and therefore of LK+(T)) with respect to first-order reasoning modulo the ground propositional lemmas of the background theory T . A third sequent calculus is introduced, LKp(T), that extends LK(T) with the possibility to polarise literals "on the fly" during proof-search. This is used in other works to simulate the DPLL(T) procedure, and we show here its completeness. Encodings of LK+(T) and LKp(T) into the most restrictive system LK(T) are presented along the way.
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https://hal.archives-ouvertes.fr/hal-00779199
Contributor : Stéphane Graham-Lengrand <>
Submitted on : Tuesday, January 22, 2013 - 1:54:34 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Long-term archiving on : Tuesday, April 23, 2013 - 3:51:20 AM

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  • HAL Id : hal-00779199, version 1

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Mahfuza Farooque, Stéphane Graham-Lengrand. Sequent Calculi with procedure calls. 2013. ⟨hal-00779199v1⟩

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