- give the properties that necessarily have not to hold and the ones that plausibly
(flexibly) have not to hold; and
- give the formulas asserting what has not (stubbornly), or may not (flexibly), be used in the definition. The notion of relevance of a formula is interesting at this stage of the definition, but instead of introducing a novel operator, we simply consider a formula as not relevant to an agent if she does not assert it. When i *asserts* a formula ϕ, she has a way to evaluate it: she thinks ϕ as positive or negative. If i does not assert ϕ then either i does not know ϕ, i.e., she is not able to evaluate it or i does not think ϕ is relevant in defining the negotiated meaning. So, we assume that whenever i thinks ϕ *as not* relevant for the negotiation, i never asserts ϕ *during the negotiation*.

Example 2 As in Example 1, consider the definition of the term "vehicle". Alice (stubbornly) thinks that it always has two, three, four or six wheels; a handlebar or a steering wheel; a motor, or two or four bicycle pedals, or a tow bar. Moreover, Alice (flexibly)
thinks that a "vehicle" may be defined only as a car, then having four wheels, a steering wheel, and a motor; or only as a bicycle, then having two wheels, a handlebar and two bicycle pedals. In other words, Alice has two acceptable ways to define a vehicle (namely, a car or a bicycle as particular "vehicles") but she has only one general description of a "vehicle". 

The necessary and the characterizing properties of a concept definition are closely related to *EGG/YOLK* objects, introduced by Lehmann and Cohn (1994) as a way to represent class membership based on typicality of the members: the egg is the set of the class members and the yolk is the set of the *typical* ones. For instance, the class of "employees" of a company A may be defined as "the set of people that receive money from the company in exchange for carrying out the instructions of a person who is an employee of that company", thus excluding, e.g., the head of the company (who has no boss), and the typical employee would include regular workers like secretaries and foremen. Another company B might have a different definition, e.g., including the head of the company, resulting in a mismatch. Nevertheless, if both companies provide some typical examples of "employees" it is possible that all of A's typical employees fit B's definition, and all of B's typical employees fit A's definition: YOLK B ≤ EGGA and YOLK A ≤ EGGB, in the terminology of (Lehmann and Cohn, 1994).

In this paper, we use the same idea to express that negotiating agents have a *preference* over their knowledge: the properties an agent thinks as necessary are the typical ones, and the characterizing properties are those that are not typical but plausible. We focus on the models of the knowledge of an agent. The stubborn properties of a concept definition are the most acceptable ones, therefore they thus have more elements satisfying them than the flexible properties have. Hence, we represent the elements satisfying the stubborn properties in the egg and those satisfying the flexible ones in the yolk. Differently from the original model, concept definitions are here restricted by stubborn properties to the largest acceptable set of models, hence represented by the egg, whilst the yolk is employed to denote the most restricted knowledge, that is, the one on which the agents are flexible.

The stubborn properties never change during the negotiation; therefore, the egg is fixed at the beginning of the MN. Instead, the flexible part of the definition of a concept is the core of the proposal of a negotiating agent. Each proposal differs from the further ones in two possible ways: it may give a definition of the negotiated object 9