Final coalgebras and the Hennessy-Milner property

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Final coalgebras and the Hennessy-Milner property
The existence of a final coalgebra is equivalent to the existence of a formal logic with a set (small class) of formulas that has the Hennessy-Milner property of distinguishing coalgebraic states up to bisimilarity. This applies to coalgebras of any functor on the category of sets for which the bisimilarity relation is transitive. There are cases of functors that do have logics with the Hennessy-Milner property, but the only such logics have a proper class of formulas. The main theorem gives a representation of states of the final coalgebra as certain satisfiable sets of formulas. The key technical fact used is that any function between coalgebras that is truth-preserving and has a simple codomain must be a coalgebraic morphism. Key words: coalgebra, final object, bisimulation, bisimilarity, congruence, ive, abstract logic
Robert Goldblatt
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where APAL
Authors Robert Goldblatt
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