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Rough set theory can be considered as the foundation of various kinds of deductive reasoning. In this paper, the authors do some logical investigations about the possibility of using partial approximation of sets as semantics of a three-valued partial logic which use one-argument predicate parameters without quantification. As a consequence of using the lower and upper approximation of sets, approximative functors appear in object language. Functors and three-valued semantics give a real possibility to investigate how to alter valid logical laws.

Some unexpected properties of partial propositional logic based on partial approximation space