Definition 6 A deductive system R is *adequate* to represent the MN process between two agents, i and j, when R infers ϕ iff for all x ∈ Ag there exists k ∈ N s.t. A
kx |= (flex kx → ϕ) ∧ (ϕ → *stub*x)
⊥ otherwise where Ag = {*i, j*} and ϕ ∈Sx∈Ag Lx.

Theorem 2 MND is adequate to represent the MN of two agents.

Proof We consider two agents that have consistent viewpoints, namely such that there exists a possible common angle. Their stubbornness sets and their flexible sets of formulas are in one of the EGG/YOLK configurations except number 1. Suppose now that the MND system infers a Σiformula ξ. Then, ξ is a common angle. Conversely, suppose that MND does not infer any Σiformula. Then, the agents are in call-away situation. Suppose now that the two agents have inconsistent viewpoints (configuration 1). The relation established is absolute disagreement. The result is that no formula can be inferred through the system, which is consistent by Theorem 1. Hence, overall, the system is adequate. 

For MN processes that are built on finite signature theories, we obtain the following decidability result:
Corollary 1 *MN is decidable for theories with finite signature under the assumption* of competitive agents.

Proof Consider an MN between competitive agents on a language with finite signature.

The number of possible proposals the agents can exchange during a MN process is formed by the possible formulas that can be built on the signature, which is finite.

Since the rules of MND are finite and the new possible proposals are finite, and the number of applications of each rule is limited to the number of proposals the other negotiator can perform, the number of steps that will be performed, in any algorithmic solution to the problem, is finite as well. 

In the following section, we extend the MND for 1-n MN in which one agent is the referee. When the Meaning Negotiation involves more than two agents, it may be viewed as an English Auction Game. An agent behaves differently if she is the auctioneer or not. The referee is the agent who receives all the proposals of the others and finds which one is shared by the agents. The auctioneer is a player himself; he makes a proposal at each new bid. The auctioneer replicates the same proposal to each of the negotiating agents. As a 1-1 MN player, the auctioneer evaluates each received proposal by testing the validity of the conditions listed above: he checks the relation between each received proposal and his stubbornness knowledge and his flexible one. An auctioneer differs from the other negotiating agents in the number of the evaluations he has to do. Moreover, when the auctioneer infers the next proposal to perform by the weakening or the changing rules, the proposal may be related in more ways than that of the proposal made by other agents. In fact, in 1-1 MN it is not possible to reach the absolute 3.2.2 MN Rules: 1-n MN