Argument, Discussion and Rationality

When applying argumentation theory for purposes of what to believe or what to do, the idea is to follow a three-step process. In the first step, one starts with a particular knowledge base and determines what are the possible defeasible derivations (called arguments) one can make using this knowledge base. These derivations then become the nodes of a directed graph called an argumentation framework. The edges of such a graph represent the attack -relation. The idea is that an argument A attacks an argument B iff what A derives somehow invalidates the derivation B. Once the argumentation framework has been constructed, the second step is to determine which of the arguments to accept. The fundamental idea of Dungs theory [1] is to determine this based purely on the structure of the graph, without looking at the actual contents of the arguments. Different selection criteria (called argumentation semantics) have been stated, often allowing for more than one possible set of accepted arguments. After determining the set (or sets) of accepted arguments, the third step in the argumentation process is to determine the set (or sets) of accepted conclusions. This can be done in a fairly straightforward way. For each accepted argument, the conclusion supported by its derivation will be an accepted conclusion. Formalisms like ABA [2] and ASPIC [3] assume that the information in the knowledge-base consists of derivation rules, where ASPIC also distinguishes between defeasible and non-defeasible (strict) derivation rules. Premises can be represented as (strict) rules with an empty antecedent. Arguments are then constructed by chaining the rules together, basically in a tree-like structure, with the premises (and assumptions) being the leaf nodes, and the conclusion of the argument being the consequent of its top-rule. A question worthwhile examining is to what extent the argumentation process can be considered to be rational. The current literature in formal argumentation allows for three approaches of examining rationality: on the semantical level (step 2) on the level of argument-based discussion, and on the level of the actual outcome of the argumentation process (step 3). As for the semantical level, we recall that the idea is, given a graph, to determine which nodes (arguments) are to be accepted and which nodes (arguments) are to be rejected. In essence, one labels each node of the graph with either accepted, rejected or undecided. Although this allows one to express any arbitrary position on which arguments are accepted, rejected or undecided, some of these positions can be considered as more reasonable than others. The role of the argumentation semantics is to determine which positions can be considered as reasonable. This is done by defining constraints on the possible argument labellings. One such constraint (called complete semantics [1, 4]) is as follows: