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A Representation Theorem for Stratified Complete Lattices

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Book cover Logic, Language, and Computation (TbiLLC 2015)

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Abstract

Stratified complete lattices are complete lattices equipped with a sequence of preorderings associated with the ordinals less than a given nonzero ordinal, typically a limit ordinal. They have been used to give semantics to recursive definitions involving nonmonotonic operations. We provide representation theorems for stratified complete lattices by inverse limits of complete lattices.

Partially supported by grant no. ANN 110883 from the National Foundation of Hungary for Scientific Research.

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Notes

  1. 1.

    The complete lattices and projections of an inverse system of [11] are continuous, and the ordinal \(\kappa \) is \(\omega \), the least infinite ordinal. Inverse systems of complete lattices over arbitrary directed partial orders are considered in [9], where following [11], the projections are usually assumed to be continuous as well.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Szeged, Szeged, Hungary

    Zoltán Ésik

Authors
  1. Zoltán Ésik
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Correspondence to Zoltán Ésik .

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Editors and Affiliations

  1. Faculty of Technology, Policy and Management, Delft University of Technology, Delft, Zuid-Holland, The Netherlands

    Helle Hvid Hansen

  2. Department of Linguistics, Cornell University, Ithaca, New York, USA

    Sarah E. Murray

  3. School of Electronic Engineering and Computer Science, Queen Mary University of London, London, United Kingdom

    Mehrnoosh Sadrzadeh

  4. Heinrich-Heine-Universität, Düsseldorf, Germany

    Henk Zeevat

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Ésik, Z. (2017). A Representation Theorem for Stratified Complete Lattices. In: Hansen, H., Murray, S., Sadrzadeh, M., Zeevat, H. (eds) Logic, Language, and Computation. TbiLLC 2015. Lecture Notes in Computer Science(), vol 10148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54332-0_15

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  • DOI: https://doi.org/10.1007/978-3-662-54332-0_15

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  • Print ISBN: 978-3-662-54331-3

  • Online ISBN: 978-3-662-54332-0

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