Modelling Argumentation: Valuations and Reasoning

This article discusses the formal modelling of argumentation. The fundamental characteristics of argumentative reasoning, which play the key role in evaluating arguments, are examined. The authors focus on the distinctive features of natural reasoning. Real practice of reasoning is frequently accompanied by usage of deductively incorrect arguments as justifications of certain statements that arise within polemical situations. Another peculiarity of natural reasoning the authors analyse consists in its nonmonotonicity, i.e., extending the set of premises of a certain valid argument affects its validity. Thus, the possibility of constructing a simple and intuitively plausible formal theory that allows grasping the aforementioned phenomena is the main aim of the article. The authors suggest a formal explication of the evidence relation between an argument and a thesis. This explication can take into account the variability of the entailment relation, i.e., allows dealing with both deductive and inductive arguments within the same framework. The suggested explication of evidence relation is substantially grounded on the notion of reasoning by modulo, which, in turn, is a suitable tool for analysing deductively incorrect arguments. The suggested explication of argumentative reasoning (critique and refutation) allows distinguishing between different kinds of nonmonotonicity (modifiability) of argumentative reasoning and, furthermore, drawing the distinction between several types of relations between premises (arguments) and conclusion (thesis): deductive reasoning by modulo, inductive consequence, and (argumentative) evidence relation.

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