Agreeing to Differ: Modelling Persuasive Dialogue Between Parties With Different Values

In some cases of disagreement, particularly in areas of practical reasoning such as ethics and law, it is impossible to provide any proof or other conclusive demonstration. The role of argument in such cases is to persuade rather than to prove, demonstrate or refute. Drawing on ideas of Perelman, we argue that persuasion in such cases relies on a recognition that the strength of an argument in these situations will vary according to its audience, and the strength accorded to an argument by an audience depends on the comparative weight that that audiences gives to the social values that the argument advances, when compared with the social values advanced by arguments competing with it. To model this we introduce the notion of Value Based Argumentation Frameworks (VAFs), an extension of Argumentation Frameworks as originally introduced by Dung. After defining VAFs we state some of their properties, and in particular we recall that in a VAF certain arguments can be shown to be acceptable however the relative strengths of the values involved are assessed. This means that disputants can agree to accept arguments, even when they differ as to which values are more important. We then describe a dialogue game based on VAFs, designed to model persuasive argumentation, which we illustrate with a widely discussed ethical problem.