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Proving implications by algebraic approximation

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Algebraic and Logic Programming (ALP 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 850))

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Abstract

This paper applies techniques of algebraic approximation to provide effective algorithms to determine the validity of universally quantified implications over lattice structures. We generalize the known result which states that any semilattice is approximated in the two element lattice. We show that the validity of a universally quantified implication ψ over a possibly infinite domain can be determined by examining its validity over a simpler domain the size of which is related to the number of constants in ψ. Both the known as well as the new results have high potential in providing practical automated techniques in various areas of application in computer science.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, PoB 653, 84105, Beer-Sheba, Israel

    Michael Codish & Grigory Mashevitzky

Authors
  1. Michael Codish
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  2. Grigory Mashevitzky
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Giorgio Levi Mario Rodríguez-Artalejo

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© 1994 Springer-Verlag

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Codish, M., Mashevitzky, G. (1994). Proving implications by algebraic approximation. In: Levi, G., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1994. Lecture Notes in Computer Science, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58431-5_4

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  • DOI: https://doi.org/10.1007/3-540-58431-5_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58431-5

  • Online ISBN: 978-3-540-48791-3

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