https://hal-mines-paristech.archives-ouvertes.fr/hal-01154799Bonichon, RichardRichardBonichonDIMAp - Departamento de Informática e Matemática Aplicada [Natal] - UFRN - Universidade Federal do Rio Grande do Norte [Natal]Hermant, OlivierOlivierHermantMINES ParisTech - École nationale supérieure des mines de Paris - PSL - Université Paris sciences et lettresA syntactic soundness proof for free-variable tableaux with on-the-fly SkolemizationHAL CCSD2015free-variable tableauxsoundnessskolemizationskolem termsfirst-order logic[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO][INFO.INFO-FL] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]Hermant, Olivier2015-05-23 15:34:502021-11-17 12:33:002015-05-23 22:24:22enPreprints, Working Papers, ...https://hal-mines-paristech.archives-ouvertes.fr/hal-01154799/documentapplication/pdf1We prove the syntactic soundness of classical tableaux with free variables and on-the-fly Skolemization. Soundness proofs are usually built from semantic arguments, and this is to our knowledge, the first proof that appeals to syntactic means. We actually prove the soundness property with respect to cut-free sequent calculus. This requires great care because of the additional liberty in freshness checking allowed by the use of Skolem terms. In contrast to semantic soundness, we gain the possibility to state a cut elimination theorem for sequent calculus, under the proviso that completeness of the method holds. We believe that such techniques can be applied to tableaux in other logics as well.