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.