Henry Prakken, Department of Information and Computing Sciences, Utrecht University and Faculty of Law, University of Groningen, The Netherlands.

Logic deals with the formal principles and criteria of validity of patterns of inference. This course discusses logics for a particular group of patterns of inference, viz. inferences that are not absolutely certain, but that can still be rationally made as long as they cannot be defeated on the basis of information to the contrary. Such patterns can be found in commonsense reasoning, i.e., the inferences humans make in their daily life, but also, for example, in legal and medical reasoning and in public debate. This kind of reasoning lacks one important property of 'standard' or 'deductive' reasoning, viz. the property of monotonicity of the consequence notion. When inferences are not absolutely certain, it may happen that conclusions inferrable from a particular body of information, are not inferrable from an extended body of information, since the new information gives rise to defeaters of the inference. Hence logics for such inference patterns are often called nonmonotonic logics.

Nonmonotonic notions of logical consequence have been studied in artificial intelligence since 1980, when the Artificial Intelligence journal published a special issue on nonmonotonic logic. Several nonmonotonic logics were proposed in this issue, the best-known of which are default logic and circumscription. This course discusses a third kind of nonmonotonic logic, based on the notion of argumentation. The first argumentation logics were proposed by the philosopher John Pollock and the AI researcher Ronald Loui. In 1995 Phan Minh Dung showed in an influential paper that argumentation can be seen as a general framework for nonmonotonic logics. In this course first Dung's fully abstract approach will be presented, after which a more concrete framework for argumentation with structured arguments is discussed.