Logical calculi of rough-set granules in problems of approximate synthesis in distributed systems

A logical calculus of granules is presented. This calculus provides a framework for the approximate synthesis of solutions under uncertainty by distributed systems. The presented calculus is based on rough mereology, a paradigm for approximate reasoning developed by the authors which blends together and relies on the mereology ideas of St. Lesniewski (see L. Polkowski and A. Skowron, Intell. Automation and Soft Comput., vol. 2, no. 2, 1996), rough set theory and fuzzy set theory.