多偏好逻辑GMPL

GMPL Logic of Kinds of Preferences

针对缺乏多类型偏好共存的偏好逻辑系统的现状,MPL(logic of many kinds of preference)被构造为一种能够表示和推理四类型偏好的偏好逻辑,但是MPL的语义基于全前序偏好结构,因而不能表示不完全偏好.为此,提出了偏好逻辑GMPL(a generalized edition of MPL).此外,通过常见逻辑偏好的GMPL重写表明GMPL较强的表达能力和实际应用前景.并提出一种将GMPL的SAT问题归结为命题逻辑的SAT问题的方法.

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.