A Note on (In)Compatibility Relations

Non-symmetric incompatibility relations, or non-symmetric compatibility relations, are a standard method for introducing a split negation pair on a frame. Another standard method is to reject commutation for the frame. The first task is to examine the relationship between non-symmetric incompatibility relations and non-symmetric compatibility relations and commutation failure on frames. The second task is to look at the sort of points that may constitute such frames. Taking the points as information states, what type of information states may operate in non-symmetric incompatibility/compatibility environments? The proposal made here is that databases consisting of sub-propositional information states, or data-points, are a respectable place to start.