Using Institutions for the Study of Qualitative and Quantitative Conditional Logics

It is well known that conditionals need a non-classical environment to be evaluated. In this paper, we present a formalization of conditional logic in the framework of institutions. In regarding both qualitative and probabilistic conditional logic as abstract logical systems, we investigate how they can be related to one another, on the one hand, and to the institution of propositional logic, on the other hand. In spite of substantial differences between these three logics, we find surprisingly clear formal relationships between them.