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CALCO
2005
Springer

The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic

13 years 9 months ago
The Least Fibred Lifting and the Expressivity of Coalgebraic Modal Logic
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.
Bartek Klin
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CALCO
Authors Bartek Klin
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