 In any logic for negation as process-exclusion, the process-exclusion will be non-directional if the logic in question is commutative. Directional process-exclusion will result when we remove the structural rule of commutation. For a discussion of the relationship between the formalisation of directional process exclusion as commutation-failure along with symmetry-failure on compatibility and incompatibility relations on information states, see Sequoiah-Grayson (2011). For an extended discussion of negative information in the context of categorial grammars, see Buszkowski (1995). 