A Review of Argumentation Based on Deductive Arguments

International audienceA deductive argument is a pair where the first item is a set of premises, the second item is a claim, and the premises entail the claim. This can be formalized by assuming a logical language for the premises and the claim, and logical entailment (or consequence relation) for showing that the claim follows from the premises. Examples of logics that can be used include classical logic, modal logic, description logic, temporal logic, and conditional logic. A counter argument for an argu-ment Ais an argument B where the claim of B contradicts the premises of A. Different choices of logic, and different choices for the precise definitions of argument and counterargument, give us a range of possibilities for formalizing deductive argumentation. Further options are available to us for choosing the arguments and counterarguments we put into anargument graph. If we are to construct an argument graph based on the arguments that can be constructed from a knowledge base, then we can be exhaustive in including all arguments and counterarguments that can be constructed from the knowledge base. But there are other options available to us. These include being selective in the arguments and counterargument we present according to a specified criterion. We consider some of the possibilities in this review and introduce properties and postulates for comparing proposals for deductive argumentation