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## When Revision-Based Case Adaptation Meets Analogical Extrapolation

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Jean Lieber
Emmanuel Nauer

#### Abstract

Case-based reasoning, where cases are described in terms of problem-solution pairs case=(x, y), amounts to propose a solution to a new problem on the basis of past experience made of stored cases. On the one hand, the building of the solution to a new problem may be viewed as a form of belief revision of the solution of a retrieved case (whose problem part is similar to the new problem) constrained by domain knowledge. On the other hand, an extrapolation mechanism based on analogical proportions has been proposed. It exploits triplets of cases (case$^a$, case$^b$, case$^c$) whose descriptions of problem parts x$^a$, $x^b$, $x^c$ form an analogical proportion with the new problem $x^tgt$ in such a way that "$x^a$ is to $x^b$ as $x^a$is to $x^gt"$. Then, the analogical inference amounts to compute a solution $y^tgt$ of $x^tgt$ by solving (when possible) an equation expressing that "$y^a$ is to $y^b$ as $y^c$ is to $y^tgt$" (where $y^a$, $y^b$ and $y^c$ are respectively the solution parts of case$^a$, case$^b$and case$^c$). The paper investigates how the belief revision view and analogical extrapolation relate. Besides that it constitutes an unexpected bridge between areas which ignore each other, it casts some light on the adaptation mechanism in case-based reasoning. The paper is illustrated by a running example.

### Dates and versions

hal-03483112 , version 1 (16-12-2021)

### Identifiers

• HAL Id : hal-03483112 , version 1
• DOI :

### Cite

Jean Lieber, Emmanuel Nauer, Henri Prade. When Revision-Based Case Adaptation Meets Analogical Extrapolation. 29th International Conference on Case-Based Reasoning (ICCBR 2021), Sep 2021, Salamanca (virtual), Spain. pp.156-170, ⟨10.1007/978-3-030-86957-1_11⟩. ⟨hal-03483112⟩

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