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A Generic Deskolemization Strategy

18 pagesPublished: May 26, 2024


In this paper, we present a general strategy that enables the translation of tableau proofs using different Skolemization rules into machine-checkable proofs. It is part of a framework that enables (i) instantiation of the strategy into algorithms for different sets of tableau rules (e.g., different logics) and (ii) easy soundness proof which relies on the local extensibility of user-defined rules. Furthermore, we propose an instantiation of this strategy for first-order tableaux that handles notably pre-inner Skolemization rules, which is, as far as the authors know, the first one in the literature. This deskolemization strategy has been implemented in the Goéland [17] automated theorem prover, enabling an export of its proofs to Coq [8] and Lambdapi [2]. Finally, we have evaluated the algorithm performances for inner and pre-inner Skolemization rules through the certification of proofs from some categories of the TPTP [39] library.

Keyphrases: automated theorem proving, Free-Variable Tableaux, proof certificate, Proof-Search Procedures, Skolemization

In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 246--263

BibTeX entry
  author    = {Johann Rosain and Richard Bonichon and Julie Cailler and Olivier Hermant},
  title     = {A Generic Deskolemization Strategy},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bj\{\textbackslash{}o\}rner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  pages     = {246--263},
  year      = {2024},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/g1tm}}
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