Logical Models of Argument.

1. MODELING ARGUMENT IN ARTIFICIAL INTELLIGENCE

Artificial intelligence (AI) has long dealt with the challenge of modeling commonsense reasoning, which almost always occurs in the face of incomplete and potentially inconsistent information [McCarthy 1984; McCarthy and Hayes 1969]. A logical model of commonsense reasoning demands the formalization of principles and criteria that characterize valid patterns of inference. In this respect, classical logic proved to be inadequate [Reiter 1980], since it behaves monotonically.

Within AI, several nonmonotonic reasoning formalisms emerged to meet this challenge. In these formalisms, conclusions drawn may be later withdrawn when additional information is obtained. Formal logics of argument emerged as one style of formalizing nonmonotonic reasoning.

The literature on nonmonotonic reasoning dominated AI's journals in the mid1980s. Oddly, the discovery of relevant philosophical, legal, and rhetorical traditions coincided with a decline in AI's purely mathematical interest in the subject as well as with a rise of international interest. Modeling argument appears to be at the foundation of AI's understanding of rule-based systems (where rules can come into conflict). It also differentiates AI's stake in representation languages (what is called knowledge representation and reasoning) from philosophical logic. At times, AI chooses logics for representation (for specification), in the same way that programmers choose programming languages. At other times, AI uses logic for analysis (for example, the way it is used in algorithms analysis). Argumentation clearly serves the former, representational use of logic in AI. AI has a particular interest in nonstandard logics. Those logics have greater expressive power, especially in a practical sense, or correspond more naturally to human linguistic convention and inferential limitation.

When a rule supporting a conclusion may be defeated by new information, it is said that such reasoning is defeasible [Nute 1988a; Pollock 1974]. When we chain defeasible reasons to reach a conclusion, we have arguments, instead of proofs. It makes sense to require defeasible reasons for argumentation. Arguments may compete, rebutting each other, so a process of argumentation is a natural result of the search for arguments. Adjudication of competing arguments must be performed, comparing arguments in order to determine what beliefs are justified. Since we arrive at conclusions by building defeasible arguments, and since mathematical argumentation has so often called itself argumentation, we sometimes call this kind of reasoning defeasible argumentation.

At first, an argument-based approach to modeling commonsense reasoning drove the development of new logical languages, resulting in new formalisms, which extended classical logic for performing nonmonotonic reasoning. At this time, argument was energetically compared with logics of counterfactual conditionals (conditional logic) and with induction.

Recently, defeasible argumentation has looked more broadly to patterns of reasoning recognized outside of mathematical logic: law, political science, rhetoric, and even scientific arguments. The result has been to recast AI's original nonmonotonic reasoning into something that pays more attention to computation.