Abstract
This paper describes an approach to case-based reasoning by which the case base is enriched at reasoning time. Enrichment results from the local application of variations to seed cases: new hypothetical cases are created which get closer and closer to the target problem. The creation of these hypothetical cases is based on structures associated to the problem and solution spaces, called variation spaces, that enable defining a language of adaptation rules. Ultimately reaching the target problem (exactly or nearly) allows the system to deliver a solution. Application of the proposed approach to machine translation shows behind state-of-the-art, but promising results.
The authors want to thank the anonymous reviewers for their detailed comments. They have tried to do their best to take them into account. The first author is supported by JSPS Grant-In-Aid 18K11447: “Self-explainable and fast-to-train example-based machine translation using neural networks”.
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Notes
- 1.
Some authors consider that analogy requires additional postulates (Lepage [10]). However, only these three postulates are used in this paper.
- 2.
When conformity is an equivalence relation, reflexivity and symmetry are straightforward. But conformity is not necessarily an equivalence relation.
- 3.
The LCS (“longest common subsequence”) distance is an edit distance based on the character insertion and character deletion edit operations, with a cost of 1 for both. In other terms, if P and Q are two strings and L is the LCS of P and Q, then \(\texttt {{dist}}(P, Q)=(|P|-|L|) + (|Q|-|L|)\).
- 4.
If uncertainty is modeled thanks to a probability measure, it is possible to associate to a probability \(P\in [0;1]\) a penalty \(\pi ={-}\log {}P\in [0;\infty ]\). If uncertainty is thought of as a measure of the gap to consistency with the real world, it is possible to associate a distance to it. Then, by definition, licit cases have a penalty of 0. The representation of uncertainty by penalties is chosen in this paper for generality of expression.
- 5.
Once again, costs could be associated to probabilities: \(\texttt {{cost}}(\texttt {{hypo}})\) could be defined by \({-}\log P(\varphi ^2~|~\varphi ^1)\), where \(P(\varphi ^2~|~\varphi ^1)\) is the probability of \(\varphi ^2\) being true given that \(\varphi ^1\) is. But they can also be associated to distance. \(\texttt {{cost}}(\texttt {{hypo}})\) could be defined as \(\texttt {{dist}}(\varphi ^1, \varphi ^2)\) which expresses the additional uncertainty on \(\varphi ^2\) when inferred from \(\varphi ^1\).
- 6.
\((\varDelta {\mathcal {P}}, {+})\) being a commutative group means that \(\varDelta {\mathcal {P}}\) is a set, that \(+\) is an associative and commutative operation on \(\varDelta {\mathcal {P}}\), and that every \(\overrightarrow{u}\in \varDelta {\mathcal {P}}\) has an inverse element \({-}\overrightarrow{u}\) (meaning \(\overrightarrow{u}+({-}\overrightarrow{u})=\overrightarrow{0}\)).
- 7.
A multiset is denoted with double braces; for example \(M=\left\{ \!\!\left\{ a, a, b, c, c, c\right\} \!\!\right\} \) contains a with multiplicity 2, b with multiplicity 1 and c with multiplicity 3. Thus the cardinality of M is \(\left| M\right| =2+1+3=6\).
- 8.
Note that this is the equality of two ratios. Of course, it is also an analogy by itself (
), but this is not what is meant here. - 9.
- 10.
https://lepage-lab.ips.waseda.ac.jp/ > Kakenhi 15K00317 > Tools.
- 11.
Remember that LCS distance is used: dist(très, trop) = 4 (two deletions and two insertions), not 2 (two substitutions) as would be the case with Levenshtein distance. .
- 12.
- 13.
), but this is not what is meant here.References
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Lepage, Y., Lieber, J. (2019). An Approach to Case-Based Reasoning Based on Local Enrichment of the Case Base. In: Bach, K., Marling, C. (eds) Case-Based Reasoning Research and Development. ICCBR 2019. Lecture Notes in Computer Science(), vol 11680. Springer, Cham. https://doi.org/10.1007/978-3-030-29249-2_16
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