  Measuring inconsistency is viewed as an important issue related to handling
inconsistencies. Good measures are supposed to satisfy a set of rational
properties. However, defining sound properties is sometimes problematic. In
this paper, we emphasize one such property, named Decomposability, rarely
discussed in the literature due to its modeling difficulties. To this end, we
propose an independent decomposition which is more intuitive than existing
proposals. To analyze inconsistency in a more fine-grained way, we introduce a
graph representation of a knowledge base and various MUSdecompositions. One
particular MUS-decomposition, named distributable MUS-decomposition leads to an
interesting partition of inconsistencies in a knowledge base such that multiple
experts can check inconsistencies in parallel, which is impossible under
existing measures. Such particular MUSdecomposition results in an inconsistency
measure that satisfies a number of desired properties. Moreover, we give an
upper bound complexity of the measure that can be computed using 0/1 linear
programming or Min Cost Satisfiability problems, and conduct preliminary
experiments to show its feasibility.
