In , 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.
A. Kurz, “Modal Rules are Co-Implications,” Electronic Notes in Theoretical Computer Science, vol. 44, no. 1, pp. 241–253, May 2001. DOI: 10.1016/S1571-0661(04)80911-3
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