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An \( \mathcal{O} \) ((n · log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic

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Automated Deduction in Classical and Non-Classical Logics (FTP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1761))

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Abstract

The provability logic Grz is characterized by a class of modal frames that is not first-order definable. We present a simple embedding of Grz into decidable fragments of classical first-order logic such as FO2 and the guarded fragment. The embedding is an \( \mathcal{O} \) ((n:log n)3)-time transformation that neither involves first principles about Turing machines (and therefore is easy to implement), nor the semantical characterization of Grz (and therefore does not use any second-order machinery). Instead, we use the syntactic relationships between cut-free sequent-style calculi for Grz, S4 and T. We first translate Grz into T, and then we use the relational translation from T into FO2.

Supported by an Australian Research Council Queen Elizabeth II Fellowship.

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Author information

Authors and Affiliations

  1. Laboratoire LEIBNIZ - C.N.R.S., 46 av. Félix Viallet, 38000, Grenoble, France

    Stéphane Demri

  2. Automated Reasoning Project and Dept. of Computer Science, Australian National University, ACT, 0200, Canberra, Australia

    Rajeev Goré

Authors
  1. Stéphane Demri
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  2. Rajeev Goré
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Editor information

Editors and Affiliations

  1. Leibniz-IMAG, 46 Avenue Felix Viallet, 38031, Grenoble cedex, France

    Ricardo Caferra

  2. Technical University of Vienna, Favoritenstraße 9-11/E185-2, 1040, Vienna, Austria

    Gernot Salzer

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Demri, S., Goré, R. (2000). An \( \mathcal{O} \) ((n · log n)3)-Time Transformation from Grz into Decidable Fragments of Classical First-Order Logic. In: Caferra, R., Salzer, G. (eds) Automated Deduction in Classical and Non-Classical Logics. FTP 1998. Lecture Notes in Computer Science(), vol 1761. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46508-1_10

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  • DOI: https://doi.org/10.1007/3-540-46508-1_10

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