The latter case prevails when there are specialists about the negotiation subject into the multiple agent system and their opinion is more relevant then the opponents' ones.

When participating to a negotiation process, the agents assume a viewpoint and many admissible angles of it. A specialist knows more about the negotiation subject than a less expert agent and her negotiation behavior will be to make concessions as few as possible. Conversely, if a no expert agent knows that an agent in the MAS is a specialist, then she trusts the specialist and probably makes concessions with respect to the proposals of the specialist. The degree of knowledge of an agent translates into the trustworthiness with respect to herself. In this paper, the trustworthiness of the agent is not specifically considered because it is out of the scope of the paper and it is left as a future work.

The role of the auctioneer is to monitor the game in order to understand when it ends and whether in a positive or a negative way. In general, the auctioneer is the first bidding agent but in a negotiation perspective she may play in two ways: active or passive. An active referee is a participant of the negotiation and the reservation price is her viewpoint. Moreover, an active referee makes herself proposals during the auction as all the other agents and she is considered in the agreement test. A passive auctioneer does not affect the negotiation. She only tests the process and makes only one bid, the first one for the reservation price.

## 1.3 Aims Of Proposed Approach

The aim of the paper is to give a general model to represent the process of MN by means of a deduction system. Our formalization is based upon Game Theory notions of behavior of the agents during a negotiation/litigation. The negotiation process has already been dealt in terms of games but, to the best of our knowledge, only quantitative negotiation were studied. MN is not quantitative thus one of the main problem in dealing with it is the identification of the agreement and disagreement situations, i.e. the mutual evaluation of the proposals of the players. The purpose of the paper is to extend the current literature with the formalization of the MN problem by means of a deduction system that is independent of the number of the involved agents and of their expression languages. Our work begins with the study of the representation of the knowledge of the agents in a MN, and in particular the representation of the properties the agents consider as necessary and unforgivable in defining the meaning of the set of terms they are negotiating and, vice versa, which are the facultative ones, because these properties identify the negotiation space between agents. We call the first one the stubborn knowledge of the agent and flexible knowledge the second one.

The *first contribution* of the paper is the definition of the meaning negotiating agent in terms of her stubborn and flexible knowledge.

The *second contribution* of the paper is the study of the agreement and disagreement situations between the agents and the definition of the different ways in which they may be in disagreement (absolute, relative, essence and compatibility).

As said above, one important issue in MN is the evaluation of a received proposal.

Agents make proposal and evaluate the opponents' one. The evaluation mechanism is not trivial when the negotiation is not quantitative. When is one definition of a set of terms better than another one? When are two or more definitions equivalent? Here, we study how a proposal is evaluated with respect to the knowledge of an agent. In our 7