This paper has two main objectives. The first objective is to give a characterization of a qualitative description of a possibility function. A qualitative description of a possibility function is called a consistent possibilistic state. The qualitative description and its characterization serve as qualitative semantics for possibility functions. These semantics are useful in representing knowledge as possibility functions. The second objective is to describe how Zadeh’s theory of possibility fits in the framework of valuation-based systems (VBS). Since VBS serve as a framework for managing uncertainty and imprecision in expert systems, this facilitates the use of possibility theory in expert systems.