Bob Kowalski

Abstract Argumentation

(paper by Bob Kowalski and Francesca Toni to appear in AI and Law)
In this work we explore the thesis that defeasible reasoning with rules of the form

P if Q

can be understood as exact reasoning with rules of the form

P if Q and S can not be shown

containing one or more defeasible non-provability claims of the form

S can not be shown.

With this understanding of defeasibility, argumentation can then be understood as a dialectic process whereby a proponent presents an exact argument of a conclusion, which is based, however, upon defeasible non-provability claims. Such a claim, and the argument it helps to support, can be defeated if an opponent can undermine the claim by presenting an argument for its contrary. Like the proponent, the opponent can also base her/his argument upon non-provability claims.

The argumentation process can be viewed, therefore, as a game in which the proponent moves first. By moving first, the proponent has the advantage of being able to use his/her previously used claims of non-provability to defeat the opponent's counter-claims.

A similar view of defeasible reasoning and argumentation has been put forward by several authors. Our approach differs, however, in several respects. The most important of these are:

(1) We focus on the acceptability of the non-provability claims of an argument, rather than on the acceptability either of the argument or of the conclusion of the argument. This abstracts from the non-contentious parts of the argument.

(2) We reduce all forms of defeasibility to that of non-provability claims. As a consequence, the only way to defeat an argument is by undermining one of its claims, namely by showing its contrary. Indirect defeat, showing that a rule

P if Q

leads to contradiction, is transformed into undermining defeat, by rewriting it in the "exact" form

P if Q and the contrary of P can not be shown.

(3) We base our formalisation upon a variant of an abstract approach to defeasible reasoning which has been shown to include many existing formalisms, including logic programming, default logic, and non-monotonic modal logic. Thus the approach is abstract and can be formalised in any one of these and other formalisms.

For more information, see http://laotzu.doc.ic.ac.uk/UserPages/staff/rak/rak.html


Maastricht Argument Day: abstracts