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On Categorial Grammatical Inference and Logical Information Systems

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Book cover Logic and Algorithms in Computational Linguistics 2018 (LACompLing2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 860))

Abstract

We consider several classes of categorial grammars and discuss their learnability. We review results where learning is viewed as a symbolic issue in an unsupervised setting, from raw or from structured data, for some variants of Lambek grammars and of categorial dependency grammars. In that perspective, we discuss for these frameworks different type connectives and structures, some limitations (negative results) but also some algorithms (positive results) under some hypothesis. On the experimental side, we also consider the Logical Information Systems approach, that allows for navigation, querying, updating, and analysis of heterogeneous data collections where data are given (logical) descriptors. Categorial grammars can be seen as a particular case of Logical Information System.

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Notes

  1. 1.

    \(^*\) in \(V^*\) is the Kleene star unary operation on V.

  2. 2.

    \(\mathbb {N}\) is the set of natural numbers \(\{0, 1, 2, 3, \ldots \}\).

  3. 3.

    Usually a lexicon is a subset of the words of a natural language and an entry is one of the words of the lexicon.

  4. 4.

    A list of entries can be compatible with none, one or several types.

  5. 5.

    Transitivity means that it is possible to derive the type \(A {/}C\) from the types \(A {/}B\) and \(B {/}C\) or the type \(A {\setminus }C\) from the types \(A {\setminus }B\) and \(B {\setminus }C\).

  6. 6.

    RG means Rigid Grammar.

  7. 7.

    Trivial classes are for instance finite sets of grammars, for which learnability is obvious.

  8. 8.

    The closure properties are satisfied as mentioned in [43]:

    \(X \vdash X^Y\), \((X^Y)^Y \vdash X^Y\), if \(X \vdash Z\) then \(X^Y \vdash Z^Y\)

  9. 9.

    www.irisa.fr/LIS/softwares.

  10. 10.

    Lefff stands for: “Lexique des Formes Fléchies du Français/Lexicon of French inflected forms” (see http://alpage.inria.fr/~sagot/lefff-en.html).

  11. 11.

    http://universaldependencies.org/format.html.

  12. 12.

    This complies with Sequoia data, but may be a simplification for other corpora.

  13. 13.

    https://universaldependencies.org/conllu_viewer.html.

  14. 14.

    http://talc2.loria.fr/grew/.

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Author information

Authors and Affiliations

  1. IRISA and Univ Rennes, Rennes, France

    Annie Foret

  2. LS2N and Univ Nantes, Nantes, France

    Denis Béchet

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  1. Annie Foret
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  2. Denis Béchet
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Correspondence to Annie Foret .

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Editors and Affiliations

  1. Department of Mathematics, Stockholm University, Stockholm, Sweden

    Roussanka Loukanova

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Foret, A., Béchet, D. (2020). On Categorial Grammatical Inference and Logical Information Systems. In: Loukanova, R. (eds) Logic and Algorithms in Computational Linguistics 2018 (LACompLing2018). Studies in Computational Intelligence, vol 860. Springer, Cham. https://doi.org/10.1007/978-3-030-30077-7_6

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