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2014 | OriginalPaper | Buchkapitel

Applying Belief Revision to Case-Based Reasoning

verfasst von : Julien Cojan, Jean Lieber

Erschienen in: Computational Approaches to Analogical Reasoning: Current Trends

Verlag: Springer Berlin Heidelberg

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Abstract

Adaptation is a task of case-based reasoning (CBR) that aims at modifying a case to solve a new problem. Now, belief revision deals also about modifications. This chapter studies how some results about revision can be applied to formalize adaptation and, more widely, CBR. Revision operators based on distances are defined in formalisms frequently used in CBR and applied to define an adaptation operator that takes into account the domain knowledge and the adaptation knowledge. This approach to adaptation is shown to generalize some other approaches to adaptation, such as rule-based adaptation.

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Vorheriges Kapitel Analogy in Automated Deduction: A Survey

Nächstes Kapitel Heuristic-Driven Theory Projection: An Overview

Calling it a metric space is an abuse of the usual mathematical language, since \(d\) does not necessarily verifies all the postulates of a distance metric. However, the term metric space is used in this chapter with this generalized meaning, for the sake of simplicity.

Once suggested by Pierre Marquis. Thanks Pierre!

This adjective is justified further in the chapter.

In the first publications about \(\mathrel {\dotplus }\)-adaptation, the term “conservative adaptation” was used for any \(\mathrel {\dotplus }\)-adaptation. Then, it has appeared that some \(\mathrel {\dotplus }\)-adaptation could hardly be qualified as conservative (see below), thus, from now on, the term of conservative adaptation is only used for revision-based adaptation using an orthogonal revision operator.

A coarse modeling of this cost is \(\mathtt{cost }(\mathrel {\mathtt{r }})=-\log {}P\) where \(P\) is the probability that \(y^{t}\) is a licit solution of \(x^{s}\). Thus, the additivity of the cost corresponds to an independence assumption of the \(q\) adaptation steps.

Some DLs use constructs that go beyond standard first-order logic, such as concrete domains, but this is not the case for \({\mathcal {ALC}}\).

\({\mathcal {U}}\) corresponds to the set of scenarios, i.e., fully constrained QCNs. \(\text {Mod}(\varphi )\) is the set of the scenarios that are more specific than the QCN \(\varphi \). A distance \(d\) between scenarios is defined. One problem is that if \(A=\text {Mod}(\psi )\) and \(B=\text {Mod}(\mu )\), \(A\mathrel {{\mathrel {\dotplus }}^{d}}B\) is not necessarily representable by a QCN (i.e., postulate (\(\mathrel {\dotplus }\)6) does not hold). In this case, to write it in a simplified manner, a most specific QCN \(\chi \) is chosen such that \(\text {Mod}(\chi )\supseteq A\mathrel {{\mathrel {\dotplus }}^{d}}B\), and \(\psi \mathrel {\dotplus }\mu =\chi \).

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Titel: Applying Belief Revision to Case-Based Reasoning
verfasst von: Julien Cojan
Jean Lieber
Verlag: Springer Berlin Heidelberg
Buch: Computational Approaches to Analogical Reasoning: Current Trends
Print ISBN: 978-3-642-54515-3

Electronic ISBN: 978-3-642-54516-0

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-3-642-54516-0_6

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