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Quantifier Elimination in Elementary Set Theory

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Relational Methods in Computer Science (RelMiCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3929))

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Abstract

In the current paper we provide two methods for quantifier elimination applicable to a large class of formulas of the elementary set theory. The first one adapts the Ackermann method [1] and the second one adapts the fixpoint method of [20]. We show applications of the proposed techniques in the theory of correspondence between modal logics and elementary set theory. The proposed techniques can also be applied in an automated generation of proof rules based on the semantic-based translation of axioms of a given logic into the elementary set theory.

Partially supported by the EU Cost Action 274 (Tarski), INTAS project 04-77-7080 and the grant 3 T11C 023 29 of the Polish Ministry of Science and Information Society Technologies.

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Author information

Authors and Affiliations

  1. National Institute of Telecommunications, Warsaw, Poland

    Ewa Orłowska

  2. The University of Economics and Computer Science, Olsztyn, Poland

    Andrzej Szałas

  3. Department of Information and Computer Science, University of Linköping, Sweden

    Andrzej Szałas

Authors
  1. Ewa Orłowska
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  2. Andrzej Szałas
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, NS, Canada

    Wendy MacCaull

  2. Department of Computer Science, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Michael Winter

  3. Computer Science Department, Brock University, L2S 3A1, St. Catharines, Ontario, Canada

    Ivo Düntsch

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Orłowska, E., Szałas, A. (2006). Quantifier Elimination in Elementary Set Theory. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_19

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  • DOI: https://doi.org/10.1007/11734673_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33339-5

  • Online ISBN: 978-3-540-33340-1

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