Monotonicity and Noise-Tolerance in Case-Based Reasoning with Abstract Argumentation

Abstract

Recently, abstract argumentation-based models of case-based reasoning (AA-CBR in short) have been proposed, originally inspired by the legal domain, but also applicable as classifiers in different scenarios. However, the formal properties of AA-CBR as a reasoning system remain largely unexplored. In this paper, we focus on analysing the non-monotonicity properties of a regular version of AA-CBR (that we call AA-CBR≽). Specifically, we prove that AA-CBR≽ is not cautiously monotonic, a property frequently considered desirable in the literature. We then define a variation of AA-CBR≽ which is cautiously monotonic. Further, we prove that such variation is equivalent to using AA-CBR≽ with a restricted casebase consisting of all “surprising” and “sufficient” cases in the original casebase. As a by-product, we prove that this variation of AA-CBR≽ is cumulative, rationally monotonic, and empowers a principled treatment of noise in “incoherent” casebases. Finally, we illustrate AA-CBR and cautious monotonicity questions on a case study on the U.S. Trade Secrets domain, a legal casebase.