Argument strength in probabilistic argumentation based on defeasible rules

Abstract

It is common for people to remark that a particular argument is a strong (or weak) argument. Having a handle on the relative strengths of arguments can help in deciding on which arguments to consider, which arguments to regard as acceptable, and on which arguments to present to others in a discussion. In computational models of argument, there is a need for a deeper understanding of argument strength. It is a multidimensional problem, and in this paper, we focus on one aspect of argument strength for deductive argumentation based on a defeasible logic. We assume a probability distribution over models of the language and consider how there are various ways to calculate argument strength based on the probabilistic necessity and sufficiency of the premises for the claim, the probabilistic sufficiency of competing premises the claim, and the probabilistic necessity of the premises for competing claims. We provide axioms for characterizing probability-based measures of argument strength, and we investigate four specific probability-based measures.