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Erschienen in:
2005 | OriginalPaper | Buchkapitel
The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic
verfasst von : Bartek Klin
Erschienen in: Algebra and Coalgebra in Computer Science
Verlag: Springer Berlin Heidelberg
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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.