Agent negotiation as proof search in linear logic

Negotiation is a key aspect of multi-agent systems, and one which clearly requires appropriate reasoning processes. Fisher [2] has introduced the notion of negotiation as theorem proving, in which the agents can reach a satisfactory arrangement iff there is proof in a given system. Fisher’s system is based on a distributed theorem proving environment employing resolution techniques in classical logic. In this paper we show how a basis in linear logic enables a richer (and arguably more natural) basis for reasoning about negotiations. In particular (i) the representation of conditionals is direct and natural in linear logic; (ii) linear logic allows for consumables to be modelled; and (iii) linear logic allows varying types of choices to be modelled in a clearer way than using classical logic. This last is of particular importance – there is an important distinction between an agent that is willing to provide clothing or food where another agent makes the choice, and an agent that is willing to provide either clothing or food but where that agent chooses between them. Hence the contribution of this paper is to provide a more natural basis for the reasoning required. In this sense our focus is on the outcome of the negotiation, rather than the (possibly argumentative) process. In particular, we assume that each party specifies what it desires, and the negotiation process presented finds solutions that satisfy all parties.