Abstract
The purpose of this paper is to summarize some of the results obtained over many years of research in proportional analogy applied to natural language processing. We recall some mathematical formalizations obtained based on general axioms drawn from a study of the history of the notion from Euclid to modern linguistics. The obtained formalization relies on two articulative notions: conformity and ratio, and on two constitutive notions: similarity and contiguity. These notions are applied on a series of objects that range from sets to strings of symbols through multi-sets and vectors, so as to obtain a mathematical formalization on each of these types of objects. Thanks to these formalizations, some results are presented that were obtained in structuring language data by the characters (bitmaps), words or short sentences in several languages like Chinese or English. An important point in using such formalizations that rely on form only, concerns the truth of the analogies retrieved or produced, i.e., whether they are valid on both the levels of form and meaning. Results of evaluation on this aspect are recalled. It is also mentioned how the formalization on string of symbols can be applied to two main tasks that would correspond to ‘langage’ and ‘parole’ in Saussurian terms: structuring language data and generating language data. The results presented have been obtained from reasonably large amounts of language data, like several thousands of Chinese characters or hundred thousand sentences in English or other languages.
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Notes
- 1.
We use this term to denote the notion. By doing this, we follow the German tradition (proportionale Analogiebildung (Osthoff 1979, p. 132) proportionale Analogiebildung (Paul 1920, p. 132) Proportionalanalogie, (Becker 1990, p. 14) The other term, analogical proportion, is usually understood as the result, i.e., the lists of forms or paradigms, (Welcomme 2010, p. 91), i.e., analogical clusters for us (see Fig. 2 or Table 1). But this last term is also used for the notion itself by some authors [e.g., Richard and Prade (2014)].
- 2.
This assumption comes from the observation of language data and formal data. It is not derived from any theoretical consideration and should thus be added to the set of basic properties for strings of symbols as such.
- 3.
The alternative proposal for the definition of proportional analogies between strings of symbols found in Stroppa (2005; Stroppa and Yvon 2004; Yvon et al. 2004) does not share the same property. That proposal allows the particular proportional analogy a : a :: ab : ba which is barred by our definition, and more generally all the proportional analogies of the type: p 1.u.s 1 : p 1.u.s 1 :: p 2.u.v.s 2 : p 2.v.u.s 2 which do not hold in general in our definition (notice the inversion of u and v in the right part of the proportion analogy although the first two members of the analogy are equal). According to that proposal, A : B :: C : D iff \( A \bullet D \cap B \bullet C \ne \emptyset \), where \( \bullet \) is the shuffle of two strings. Now,
$$ \left\{ \begin{gathered}a.ba = aba{\kern 1pt} \in a \bullet ba \hfill \\ ab.a = aba{\kern 1pt} \in a \bullet ab \end{gathered} \Rightarrow a \bullet ba \cap a \bullet ab \ne \emptyset \hfill \\ \right. $$(9)and
$$ \left\{ \begin{gathered} p_{1} .p_{2} .u.vu.s_{1} .s_{2} = p_{1} p_{2} uvus_{1} s_{2} {\kern 1pt} \in A \bullet D\, \hfill \\ p_{1} .p_{2} .uv.u.s_{1} .s_{2} = p_{1} p_{2} uvus_{1} s_{2} {\kern 1pt} \in B \bullet C \end{gathered}\Rightarrow A \bullet D \cap B \bullet C \ne \emptyset \hfill \\ \right. $$(10)Consequently, our definition of proportional analogy between strings of symbols puts more constraints on parallel infixing thanks to the limitations induced by distances.
- 4.
This is also trivially implied by the definition mentioned in the above footnote.
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Acknowledgments
I would like to mention the contribution of many colleagues, researchers or students in getting many of the experimental results presented here over the years. They are listed in alphabetical order below: Nicolas Auclerc, Etienne Denoual, Chooi Ling Goh, Erwan Guillerm, Juan Luo, Jin Matsuoka, Kota Matsushita, Julien Migeot, Guilhem Peralta, Kota Takeya, Hao Wang, Wei Yang.
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Lepage, Y. (2015). Proportional Analogy in Written Language Data. In: Gala, N., Rapp, R., Bel-Enguix, G. (eds) Language Production, Cognition, and the Lexicon. Text, Speech and Language Technology, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-08043-7_10
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