Monadic extensions of institutions

In this paper we show how partially ordered monads can be used to provide a non-classical extension of institutions and entailment systems as appearing in the framework of general logics. General logics is an axiomatization of a general framework for logics. This framework builds upon traditional power sets of sentences as appearing in satisfaction relations and entailment. The underlying power set monad is implicit, and the utility of a monadic machinery was therefore not explored. Making the use of the power set monad more explicit in the satisfaction and entailment relations opens up possibilities to experiment with various non-classical representations of sentences as appearing in inference. These representations are enabled by partially ordered monads, where the partial order attached to the underlying set functor is essential for extending the axiomatization.