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This article is conceived as a homage to mathematicians andcomputer theorists working on basic concepts concerning knowledge andtheir usage in application contexts. Due to their work, we now have in ourpossession very impressive tools for analysis of uncertainty like rough settheory and fuzzy set theory along with hybrid ramifications between thetwo and with other areas of research in the realm of cognitive technologiesin particular a very promising area of cognitive informatics. In this work, we strive at presenting basic issues in granular theory ofknowledge emphasizing formal aspects of our approach. This approachcan be seen as a continuation of the line of analysis initiated by GottlobFrege with his idea of exact and inexact concepts through analysis of theidea of knowledge by Popper, Lesniewski, Łukasiewicz and others, to theimplementation of the Fregean idea in the theory of knowledge knownas rough set theory initiated by Pawlak and pursued by many followers. The basic tool in our analysis of the idea of a concept and a fortioriof knowledge is mereological theory of concepts (Lesniewski): we try toconvince the reader that ideas of that theory suit well needs of analysisof knowledge and granulation of it. This work arises from some previous attempts at developing this ideasin a wider context of ontological discussion; the author is indebted to thecolloquia series SEFIR at Lateran University in Rome, where he was ableto present the basic ideas in a lecture in January 2005; for this opportunityhe is grateful to Professors Giandomenico Boffi and Alberto Pettorossi. The author wishes to dedicate this work to the memory of ProfessorsHelena Rasiowa and Zdzisław Pawlak who influenced very much hisresearch interests in this area.