Modal Languages for Coalgebras in a Topological Setting

AbstractIt is well know that the solution Z of a recursive domain equation, given by an endofunctor T, is the final T-coalgebra. This suggests a coalgebraic approach to obtain a logical representation of the observable properties of Z. The paper considers fibrations of frames and (modal) logics, arising through a set of predicate liftings. We discuss conditions, which ensure expressiveness of the resulting language (denotations of formulas determine a base of the frame over the final coalgebra). The framework is then instantiated with categories of domains, and we establish these conditions for a large class of locally continuous endofunctors. This can be seen as abs1.texa first step towards a final perspective on Abramsky's domain theory in logical form