Compatibility and Implication from a Non-Classical Perspective

This paper draws attention to key logical relations between two distinct and indepen- dently intelligible notions, compatibility and implication. We identify a set of inference rules governing compatibility and show how crucial principles concerning condition- als can be derived from these rules, on the assumption that implication is definable in terms of compatibility. As will emerge — and this is the main point of the paper — the logical relations considered are to a large extent neutral as to the underlying logic, as they hold in a wide range of non-classical systems.