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International Conference on Algebra and Coalgebra in Computer Science

CALCO 2005: Algebra and Coalgebra in Computer Science pp 247–262Cite as

The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3629))

Abstract

Every endofunctor B on the category Set can be lifted to a fibred functor on the category (fibred over Set) of equivalence relations and relation-preserving functions. In this paper, the least (fibre-wise) of such liftings, L(B), is characterized for essentially any B. The lifting has all the useful properties of the relation lifting due to Jacobs, without the usual assumption of weak pullback preservation; if B preserves weak pullbacks, the two liftings coincide. Equivalence relations can be viewed as Boolean algebras of subsets (predicates, tests). This correspondence relates L(B) to the least test suite lifting T(B), which is defined in the spirit of predicate lifting as used in coalgebraic modal logic. Properties of T(B) translate to a general expressivity result for a modal logic for B-coalgebras. In the resulting logic, modal operators of any arity can appear.

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Author information

Authors and Affiliations

  1. University of Sussex, Warsaw University,  

    Bartek Klin

Authors
  1. Bartek Klin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    José Luiz Fiadeiro

  2. Department of Computer Science, University of Wales Swansea, SA2 8PP, Swansea, UK

    Neil Harman

  3. University of Wales Swansea, United Kingdom

    Markus Roggenbach

  4. CWI and Vrije Universiteit Amsterdam,  

    Jan Rutten

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Klin, B. (2005). The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic. In: Fiadeiro, J.L., Harman, N., Roggenbach, M., Rutten, J. (eds) Algebra and Coalgebra in Computer Science. CALCO 2005. Lecture Notes in Computer Science, vol 3629. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548133_16

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  • DOI: https://doi.org/10.1007/11548133_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28620-2

  • Online ISBN: 978-3-540-31876-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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