Cautious Monotonicity in Case-Based Reasoning with Abstract Argumentation

Recently, abstract argumentation-based models of case-based reasoning ($AA{\text -}CBR$ in short) have been proposed, originally inspired by the legal domain, but also applicable as classifiers in different scenarios, including image classification, sentiment analysis of text, and in predicting the passage of bills in the UK Parliament. However, the formal properties of $AA{\text -}CBR$ as a reasoning system remain largely unexplored. In this paper, we focus on analysing the non-monotonicity properties of a regular version of $AA{\text -}CBR$ (that we call $AA{\text -}CBR_{\succeq}$). Specifically, we prove that $AA{\text -}CBR_{\succeq}$ is not cautiously monotonic, a property frequently considered desirable in the literature of non-monotonic reasoning. We then define a variation of $AA{\text -}CBR_{\succeq}$ which is cautiously monotonic, and provide an algorithm for obtaining it. Further, we prove that such variation is equivalent to using $AA{\text -}CBR_{\succeq}$ with a restricted casebase consisting of all "surprising" cases in the original casebase.