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.

Argumentation-Based Reasoning with Preferences

“…if B is less preferred than A (in symbols, B A), then B A fails; see e.g. [1,6,9,12,21,22,24,27,33]. Some formalisms (e.g.…”

“…We begin with a well known formalism called Deductive Argumentation [8,9] in which classical logic is commonly used as a basis. Deductive Argumentation can be seen as a representative of those formalisms that employ forms of propositional, first-order, conditional or temporal logics, e.g.…”

“…Deductive Argumentation can be seen as a representative of those formalisms that employ forms of propositional, first-order, conditional or temporal logics, e.g. [1,8,9,22,25].…”

“…Hence the variety of formalisms of argumentation with preferences: e.g. [1,3,5,6,9,12,21,22,24,27,30,32,33,36,37].…”

Towards a framework for computational persuasion with applications in behaviour change1

“…negates the support of the argument). A range of options for structured argumentation at the logic level have been investigated (see [17,51,104,140] for tutorial reviews of some of the key proposals. Whilst most proposals for structured argumentation involve simple rule-based reasoning, there is some investigation of the role of classical logic in argumentation (see for example [16]), and of how probabilistic reasoning can be incorporated in structured arguments (see for example [74,139,144]).…”