An institutional approach to positive coalgebraic logic.

Positive modal logic, as introduced by Dunn in 1995, is the negation-free fragment of the standard modal logic of all Kripke frames. Positive coalgebraic logic, introduced by the authors in a previous work, expands the above result from Kripke frames to more general transition systems, namely to coalgebras of weak-pullback preserving functors. We show that this construction is both modular and uniform in the functor giving the type of coalgebra. More precisely, we formalize both Set and Pos-based coalgebraic modal logic as institutions, and we exhibit a morphism of institutions between them giving the positive fragment of coalgebraic modal logic. [ABSTRACT FROM AUTHOR]