Abstract To approximate sets a number of theories have appeared for the last decades. Starting up from some general theoretical pre-conditions the authors give a set of minimum requirements for the lower and upper approximations and define general partial approximation spaces. Then, these spaces are applied in logical investigations. The main question is what happens in the semantics of the first-order logic when the approximations of sets as semantic values of predicate parameters are used instead of sets as their total interpretations. On the basis of defined partial interpretations, logical laws relying on the defined general set-theoretical framework of set approximation are investigated
