Modal Rules are Co-Implications
Alexander Kurz · Electronic Notes in Theoretical Computer Science · 2001
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.