In this paper I argue that to explain and resolve some kinds of disagreement we need to go beyond what logic alone can provide. In particular, following Perelman, I argue that we need to consider how arguments are ascribed different strengths by different audiences, according to how accepting these arguments promotes values favoured by the audience to which they are addressed. I show how we can extend the standard framework for modelling argumentation systems to allow different audiences to be represented. (...) I also show how this formalism can explain how some disputes can be resolved while in others the parties can only agree to differ. I illustrate this by consideration of a legal example. Finally, I make some suggestions as to where these values come from, and how they can be used to explain differences across jurisdictions, and changes in views over time. (shrink)

We study the semantics of dialectical proof procedures. As dialectical proof procedures are in general sound but not complete wrt admissibility semantics, a natural question here is whether we could give a more precise semantical characterization of what they compute. Based on a new notion of infinite arguments representing loops, we introduce a stricter notion of admissibility, referred to as strict admissibility, and show that dialectical proof procedures are in general sound and complete wrt strict admissibility.

The first issue of _Artificial Intelligence and Law_ journal was published in 1992. This paper provides commentaries on landmark papers from the first decade of that journal. The topics discussed include reasoning with cases, argumentation, normative reasoning, dialogue, representing legal knowledge and neural networks.