A formal approach to Perception Calculus of Zadeh by means of rough mereological logic

Rough set theory is a paradigm for approximate reasoning based on the assumption that concepts are divided into exact and non–exact (called also rough) ones by means of a topological structure induced by a representation of knowledge as a classification. A classification in its most simple form is an equivalence relation on a universe of objects; the classification induces a partition topology and concepts (meant as subsets of the universe) that are clopen are exact whereas other concepts are rough. In consequence, rough sets are represented as pairs of exact sets of the form (interior, closure). Investigations into deeper structures resulting from that assumption have led to an idea of rough mereology. On this ground also possibility for intensional many–valued logics has been recognized that have been called rough mereological logics. In this contribution, we present a development of rough mereological logics and we propose an application for these logics as a framework within which Calculus of Perceptions outlined by Zadeh may be given a formal rendering as a tool for semantic interpretation of vague statements.