  In a multigranular framework, the two most important binary predicates are
those for subsumption and disjointness. In the first part of this work, a sound
and complete inference system for assertions using these predicates is
developed. It is customized for the granular framework; particularly, it models
both bottom and top granules correctly, and it requires all granules other then
the bottom to be nonempty. Furthermore, it is single use, in the sense that no
assertion is used more than once as an antecedent in a proof.
  In the second part of this work, a method is developed for extending a sound
and complete inference system on a framework which admits Armstrong models to
one which provides sound and complete inference on all assertions, both
positive and negative. This method is then applied to the binary granule
predicates, to obtain a sound and complete inference system for subsumption and
disjointness, as well as their negations.
