Reasoning consistently about inconsistency

Patching et al. and Hinde et al. in their work on truth-space mass assignments, presented a semantic unification function and a semantic separation function for mass assignment logic that dealt with inconsistency. This paper takes these two functions and while preserving the outside inconsistencies shows how inconsistency can be reasoned about in a consistent manner. This means that inconsistency that arises outside the system need not enter the system, but needs to be represented within the system, and can therefore be extracted appropriately as output from the system to emerge as inconsistency on the outside. The internal reasoning system need therefore only concern itself with belief in truth, falsity and uncertainty.