an inference engine whose derivations are indeed agreement processes. This approach views meaning negotiation as an inference process.

To clarify what a negotiation process indeed is, let us introduce an example that we will also employ in the rest of the paper as a running example.

Example 1 Consider two agents Alice and Bob that the negotiate the meaning of the term "vehicle". Suppose that Alice thinks that a vehicle 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. On the other hand, Bob thinks that it always has two, three or four wheels; a handlebar or a steering wheel; a motor, or two or four bicycle pedals. Alice and Bob are in disagreement because Bob does not know if a vehicle has a tow bar or not. 

In this example, the MN depends upon the relevance of the terms the agents use.

Alice and Bob define "vehicle" in different ways and with different terms. In fact, Alice uses "tow bar" and Bob does not. Bob does not say anything about the tow bar maybe he does not know what a tow bar is, or maybe he does not consider as relevant the properties about the tow bar. In this paper, we assume that the agents make assertions only about the properties they consider as relevant.

One of the main parameters of the MN is the number of the involved agents. In Section 1.1, we discuss in detail how a negotiation process takes place between two parties, whilst in Section 1.2 we discuss the situation arising when the number of involved partners is higher than two.

Before we do so, we further exemplify the specific problems of the definition of an inference engine, by considering a case taken from a common situation. We consider the Description Logic framework, where the notion of term, and definitions, in particular, of term, is part of the structure itself of the Logic. More specifically, in description logic, the *acceptability* of a concept is tested by the subsumption relation. Having two concepts A and B, A subsumes B (A v B) when the definition for B is also a definition for A but not vice versa. Two concepts are equivalently defined when A v B and B v A. Suppose that Alice considers A and B, where A v B, as two plausible definitions for a concept X. Alice can accept a new definition C for X iff A v C v B because Alice has a pair of concepts (*A, B*) describing the same things that C describes.

In the same way of the above mentioned Description Logic Framework, a logical formula ϕ is acceptable with respect to an agent when she shares the interpretation of all its terms. Therefore Alice always accepts ϕ when it is equivalent to her current angle α, that is α ↔ ϕ because I(α) = I(ϕ) where I is an interpretation function, but Alice will accept ϕ also when she has a pair of feasible angles α and β such that α → ϕ → β because I(α) ⊆ I(ϕ) ⊆ I(β). In the last case Alice shares the interpretation of all the terms in ϕ by means of two angles α and β that are partial representations of her knowledge she considers as acceptable.

An agent always accepts a logical theory when it is equivalent to her own one, i.e.

when the two theories have the same set of semantical models. The logical equivalence is always a condition of agreement but there are situations in which it is not a necessary condition and some weaker conditions are sufficient to claim the agreement. In fact, a logical theory may be considered acceptable when it is a good compromise for an agent, i.e the logical theory expresses an acceptable part of what the agent wants to express. In this sense, the set of semantical models of the proposal is not equal to the set of semantical models of the theory of the agent, but the agent has a superset and a subset of models bounding it.

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