Abstract Conditional preference networks (CP-nets)is a popular language which represents qualitative conditional preference relation. Aiming at the problem that graphical representation is not enough to fulfill operations on CP-nets, an algebraic representation of CP-nets is offered with the well-known adjacent list approach. In the approach, vertical nodes are organized by topological order, and horizontal nodes are organized by their parents. Particularly, conditional preference table of nodes are represented by main disjunctive normal form of proposition logic. A direct model solving algorithm is devised later, and an indirect model solving algorithm is gotten based on relation operation on direct model. In short, the representation approach reveals that CP-nets can be not only represented by simple and intuitive graphical approach, but also represented by compacted algebraic approach.
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