Compatibility and Implication from a Non-Classical Perspective

This paper draws attention to key logical relations between two distinct and independently intelligible notions, compatibility and implication . We identify a set of inference rules governing compatibility and show how crucial principles concerning conditionals 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.