In this paper, we examine many real world examples of information granules, and construct a granular deductive reasoning system for these domains. Objects are ordered pairs; the first element is an assertion (to call logical formula) and the second is a semantic set corresponding to the assertion. So the granular language and its model involve both logic and set theory. So-called logic means that the reasoning obeys the syntax in logical language; So called set theory means that the operations corresponding to semantic sets of logical formulas obey the methods in set theory. The evaluation of truth values and the computation rule of granular formulas are established.
Qing Liu, Qing Liu,
"Granular language and its reasoning", Proc. SPIE 5098, Data Mining and Knowledge Discovery: Theory, Tools, and Technology V, (21 March 2003); doi: 10.1117/12.509163; https://doi.org/10.1117/12.509163