- Information sources are mutually independent;
- All sources exhibit the same level of importance;
- The level of information importance is also constant.

The main assumption regards the completely reliance of all the information sources as in (Booth, 2006). More realistic approaches suppose that the information sources are not equally reliable and that some source is preferred with respect to the available ones. In (Gr´egoire, 2006) the reliability of the information sources is defined as a preference order. Another precedent approach assume a weight applied to the beliefs for each source by which they belong (Lin, 1996).

In the situations in which the information sources are equally reliable, the merging is said *non-prioritized* otherwise a degree of certainty or plausibility is given to the belief (Ferm´e and Rott, 2004).

When the beliefs coming from the different sources, they have to be merged in order to *minimally change* the initial knowledge base. The operation needed to add new information into a knowledge base is known as *revision* and it involves only conflicting beliefs during a negotiation process. The general approach of *maximal adjustment* is to remove the present belief causing the conflict and adding the new one. In (Benferhat et al, 2004) the author present a *disjunctive maximal adjustment* in which the belief are weighted and thus not always removed or simply added into the knowledge base.

The merging2of beliefs was defined by two operators (Liberatore and Schaerf, 1998): *majority* and *arbitration*. Both make assumptions upon the information sources.

The former revises the knowledge base by belief belonging to the majority number of information sources. The latter revises the knowledge bases by the beliefs belonging to the most reliable information sources.

In (Konieczny, 2000) the author defines the postulates regulating the merging operators by assuming that there are *integrity constraints* to assure.

Thus, in a belief merging and information fusion literature, the negotiation is modeled as a two stage processes: contraction of the beliefs causing the conflict and expansions by the new knowledge (Booth, 2006). In (Zhang et al, 2004) the author define a way to formalize the negotiation process as a function and he proposes a set of postulates, similar to the AGM ones for revision for the negotiation function.

## 5 Conclusions

We presented a formalization of the MN problem by means of a deduction system. As we remarked in many different places of the paper, the literature has dealt with several issues of the negotiation of meaning, but what has been only partially treated is the description of the process of reaching agreement conditions.

Here, we focused upon the MN problem in terms of knowledge representation and of automatic mechanism of reaching an agreement. First, we defined a negotiating agent by two set of knowledge: stubborn and flexible. The stubborn knowledge of the agent is the unquestionable one and it represents the necessary properties to define the meaning of the set of terms the agent is negotiating. Instead, the flexible knowledge 2 One can be tempted to assume that arbitration and majority operators can be fruitfully employed to solve any admissible problem of negotiation. However, negotiation is the process of reaching agreements not the underlying semantic theory about the models. Therefore, although we can model the resulting theory by the theory of belief revision, negotiation processes are out of scope in these theories.