Coalgebraic Logic

Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviors of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss's coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss's logic. The three logics are equivalent for a natural but restricted class of functors. We give examples showing that the logics fall apart in general. Finally, we argue that the quest for a generic logic for T-coalgebras is still open in the general case.

• Type: Journal
• Year: 1999
• Where: APAL
• Authors: Lawrence S. Moss
• Keywords: APAL 1999, Coalgebraic Logic, Functors, Logic