A concept is decided by a subset of attributes

and then a Boolean function presents a concept.A given property P corresponds a class C of Boolean functions with the property P.The deciding problem whether or not a function f has the property P is transformed into deciding f∈C.For testing the property of the function f

an usual method is reconstructing an approximation functionhby sampling from C

and the property of f is described approximately by the property of h.The process of reconstructing h is called as the learning of f.It presents that the theory and method of the learning and testing of properties for Boolean functions

and it can be applied to the learning of concepts and the learning and testing of functions with given properties.