Abstract. Many autonomous agents operate in domains in which the cooperation of their fellow agents cannot be guaranteed. In such domains negotiation is essential to persuade others of the value of co-operation. This paper describes a general framework for negotiation in which agents exchange proposals backed by arguments which summarise the reasons why the proposals should be accepted. The argumentation is persuasive because the exchanges are able to alter the mental state of the agents involved. The framework is inspired by our work in the domain of business process management and is explained using examples from that domain. Keywords: Automated negotiation, Argumentation, Persuasion. 1

... In passing we establish an upper bound for a related number D(G, G0), the minimum quantifier depth of a first order sentence which is true on exactly one of graphs G and G0. If G and G0 are non-isomorphic and both have n vertices, then D(G, G0) < = (n + 3)/2. This bound is tight up to an additive constant of 1. If we additionally require that a sentence distinguishing G and G0 is existential, we prove only a slightly weaker bound D(G, G0) < = (n + 5)/2.

Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability overfinite structures, motivated by the correspondence between uniform AC and FO(PLUS;TIMES). We prove finite analogs of three classic results in arithmetical definability, namely that < and TIMES can first-order define PLUS, that < and DIVIDES can first-order define TIMES, and that < and COPRIME can first-order define TIMES.

We develop a variant of Least Fixed Point logic based on First Order logic with a relaxed version of guarded quantification. We develop a Game Theoretic Semantics of this logic, and find that under reasonable conditions, guarding quantification does not reduce the expressibility of Least Fixed Point logic. But guarding quantification increases worst-case time complexity.

Many descriptive and computational complexity classes have game-theoretic representations. These can be used to study the relation between different logics and complexity classes in finite model theory.