Constructing argument graphs with deductive arguments: a tutorial

Abstract

A 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 formalised 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 counterargument for an argument A is 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 formalising deductive argumentation. Further options are available to us for choosing the arguments and counterarguments we put into an argument graph. If we are to construct an argument graph based on the arguments that can be constructed from a knowledgebase, then we can be exhaustive in including all arguments and counterarguments that can be constructed from the knowledgebase. But there are other options available to us. We consider some of the possibilities in this review.

Keywords:

• structured argumentation
• logic-based argumentation
• deductive arguments

Acknowledgements

The authors are very grateful to Henry Prakken for some very interesting and valuable discussions on the nature of deductive argumentation. The second author is also grateful to Schloss Dagstuhl, and the organisers and participants of the seminar on Belief Change and Argumentation in Multi-Agent Scenarios (Seminar 13231), for giving him the opportunity to discuss some of the ideas in this tutorial.