Because of the absence of a whole logic to represent and reason various kinds of preferences, MPL (logic of many kinds of preference) is presently constructed to fill the gap. But, the semantics of MPL is based on the complete pre-order, so incomplete preferences cannot be expressed in it. In this paper, GMPL (a generalized edition of MPL) is introduced to supply the gap. In addition, the expressive power of GMPL is showed by rewriting several familiar logical preferences. Moreover, a decision procedure is introduced to reduce SAT problem of GMPL into that of propositional logic.