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In [13], it was shown that modal logic for coalgebras dualises—concerning definability— equational logic for algebras. This paper establishes that, similarly, modal rules dualise implications:It is shown that a class of coalgebras is definable by modal rules iff it is closed under H (images) and Σ (disjoint unions). As a corollary the expressive power of rules of infinitary modal logic on Kripke frames is characterised.


This article was originally published in Electronic Notes in Theoretical Computer Science, volume 44, number 1, in 2001. DOI: 10.1016/S1571-0661(04)80911-3



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