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Andrews Skolemization May Shorten Resolution Proofs Non-elementarily

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Logical Foundations of Computer Science (LFCS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13137))

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Abstract

In this paper we construct a sequence of formulas \(F_1, F_2, \ldots \) with resolution proofs \(\pi _1, \pi _2, \ldots \) of these formulas after Andrews Skolemization, such that there is no elementary bound in the complexity of \(\pi _1, \pi _2, \ldots \) of resolution proofs \(\pi '_1, \pi '_2, \ldots \) after structural Skolemization. The proofs are based on the elementary relation of resolution derivations with Andrews Skolemization to cut-free \(\mathbf{LK}^{+}\)-derivations and of resolution derivations with structural Skolemization to cut-free \(\mathbf{LK}\)-derivations. Therefore, this paper develops an application of the concept of only globally sound calculi to automated theorem proving.

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Notes

  1. 1.

    In the negated formula, strong quantifiers are positive existential and negative universal quantifiers, and weak quantifiers are negative existential and positive universal quantifiers. (Otherwise, strong quantifiers are positive universal and negative existential quantifiers, and weak quantifiers are negative universal and positive existential quantifiers.).

  2. 2.

    Prenexification before Skolemization is not recommendable [5].

References

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Author information

Authors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, TU Wien, Wien, Austria

    Matthias Baaz

  2. Institute of Logic and Computation, TU Wien, Wien, Austria

    Anela Lolic

Authors
  1. Matthias Baaz
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  2. Anela Lolic
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Correspondence to Anela Lolic .

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Editors and Affiliations

  1. CUNY Graduate Center, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

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Baaz, M., Lolic, A. (2022). Andrews Skolemization May Shorten Resolution Proofs Non-elementarily. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2022. Lecture Notes in Computer Science(), vol 13137. Springer, Cham. https://doi.org/10.1007/978-3-030-93100-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-93100-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-93099-8

  • Online ISBN: 978-3-030-93100-1

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