Final coalgebras and the Hennessy–Milner property

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• 作者：Robert Goldblatt
• 关键词：Coalgebra ; Final object ; Bisimulation ; Bisimilarity ; Congruence ; Coinductive ; Abstract logic
• 刊名：Annals of Pure and Applied Logic
• 出版年：2006
• 出版时间：March 2006
• 年：2006
• 卷：138
• 期：1-3
• 页码：77-93
• 全文大小：261 K

文摘

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.