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

• URL: http://arxiv.org/abs/2107.06413v1
• Date: Tue, 13 Jul 2021 22:10:24 GMT
• Title: Monotonicity and Noise-Tolerance in Case-Based Reasoning with Abstract Argumentation (with Appendix)
• Abstract summary: We prove that $AAtext - CBR_succeq$ is not cautiously monotonic. We show that this variation of $AAtext - CBR_succeq$ is cumulative, rationally monotonic, and empowers a principled treatment of noise in "incoherent" casebases.
• Score: 12.932177565788976
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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