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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Reasoning with Rough Inclusions: Granular Computing, Granular Logics, Perception Calculus, Cognitive and MAS Reasoning
verfasst von : Lech Polkowski
Erschienen in: Approximate Reasoning by Parts
Verlag: Springer Berlin Heidelberg
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Rough mereology allows for a plethora of applications in various reasoning schemes due to universality of its primitive predicate of a part to a degree. We have already stressed that by its nature, rough mereology is especially suited to reasoning with collective concepts like geometric figures or solids, or, concepts learned by machine learning methods, i.e., with collective concepts. Those applications are presented in Ch. 8 and Ch. 9. In this chapter, we begin this discussion with a formal approach to the problem of granulation of knowledge and then we examine rough mereological logics: from our results in Ch. 6 it follows that representing implication with a rough inclusion
μ
leads to logics which extend and generalize fuzzy logics. As an application, we propose a formal rendering of the idea of perception calculus, due to Zadeh [67]. We apply rough mereological schemes to reasoning by multi–agent (MAS) systems, and finally we present a rough mereological variant of cognitive reasoning in neural–like systems.