We introduce Supported Abstract Argumentation for Case-Based Reasoning (sAA-CBR), a binary classification model in which past cases engage in debates by arguing in favour of their labelling and attacking or supporting those with opposing or agreeing labels. With supports, sAA-CBR overcomes the limitation of its precursor AA-CBR, which can contain extraneous cases (or spikes) that are not included in the debates. We prove that sAA-CBR contains no spikes, without trading off key model properties

Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between arguments including support and attack relationships. In this paper, we assume that an argument map contains the premises and claims of arguments, and support and attack relationships between them, that have been identified by argument mining. So from a piece of text, we assume an argument map is obtained automatically by natural language processing. However, to understand and to automatically analyse that argument map, it would be desirable to instantiate that argument map with logical arguments. Once we have the logical representation of the arguments in an argument map, we can use automated reasoning to analyze the argumentation (e.g. check consistency of premises, check validity of claims, and check the labelling on each arc corresponds with thw logical arguments). We address this need by using classical logic for representing the explicit information in the text, and using default logic for representing the implicit information in the text. In order to investigate our proposal, we consider some specific options for instantiation.

Case-based reasoning is known to play an important role in several legal settings. In this paper we focus on a recent approach to case-based reasoning, supported by an instantiation of abstract argumentation whereby arguments represent cases and attack between arguments results from outcome disagreement between cases and a notion of relevance. In this context, relevance is connected to a form of specificity among cases. We explore how relevance can be learnt automatically in practice with the help of decision trees, and explore the combination of case-based reasoning with abstract argumentation (AA-CBR) and learning of case relevance for prediction in legal settings. Specifically, we show that, for two legal datasets, AA-CBR and decision-tree-based learning of case relevance perform competitively in comparison with decision trees. We also show that AA-CBR with decision-tree-based learning of case relevance results in a more compact representation than their decision tree counterparts, which could be beneficial for obtaining cognitively tractable explanations.

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. 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. We then define a variation of $AA{\text -} CBR_{\succeq}$ which is cautiously monotonic. Further, we prove that such variation is equivalent to using $AA{\text -} CBR_{\succeq}$ 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 $AA{\text -} CBR_{\succeq}$ is cumulative, rationally monotonic, and empowers a principled treatment of noise in "incoherent" casebases. Finally, we illustrate $AA{\text -} CBR$ and cautious monotonicity questions on a case study on the U.S. Trade Secrets domain, a legal casebase.

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.