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Logic and Algorithms in Computational Linguistics 2018 (LACompLing2018) pp 67–93Cite as

From Tree Adjoining Grammars to Higher Order Representations of Abstract Meaning Representations via Abstract Categorial Grammars

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

Abstract

We construct an Abstract Categorial Grammar (ACG) that interrelates Tree Adjoining Grammar (TAG) and Higher Order Logic (HOL) formulas encoding Abstract Meaning Representations (AMRs). We also propose another ACG that interrelates TAG and HOL formulas expressing neo-Davidsonian event semantics. Both of these encodings are based on the already existing ACG encoding of the syntax–semantics interface where TAG derivations are interpreted as HOL formulas representing Montague semantics. In particular, both of these encodings share the same abstract language coming from the ACG encoding of TAG with Montague semantics, which is second-order. For second-order ACGs, problems of parsing and generation are known to be of polynomial complexity. Thus we get the natural language generation and parsing with TAGs and HOL formulas modelling AMRs for free.

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Notes

  1. 1.

    Sayeed and Demberg [27] propose to construct neo-Davidsonian semantics from TAG.

  2. 2.

    Of course, one may use just \( \lambda \) in both cases, but sometimes, it is helpful to see which variable is linear and which one is not, only by looking at the term (otherwise, the type of a term already makes it explicit what is linear and what is not).

  3. 3.

    Not to be confused with the notion of a second-order signature, even though these two notions can be related to each other.

  4. 4.

    Pogodalla [24, 25] shows how to encode other kinds of sentences in the same principled way and thus one can easily give an account to them here as well.

  5. 5.

    Such an approach to encode semantic forms is not new: in fact, Pogodalla [23] presents an approach where underspecified formulas built using labels are encoded within a HOS, and TAG derivation trees are interpreted as those formulas. The main difference between underspecified labelled formulas and the ones of neo-Davidsonian event semantics is that underspecified labelled formulas may give rise to several semantic formulas when specified (when constraints are properly met). In contrast, a formula of neo-Davidsonian event semantics is already a fully determined semantic formula. Nevertheless, they have much in common, because one can see events as labels, or put it in another way, a formula of neo-Davidsonian event semantics can be seen as an underspecified labelled formula that gives rise to a single formula.

  6. 6.

    ACG files encoding grammars and examples provided in Sect. 6 can be found at the following link: https://github.com/GU-CLASP/ACG-AMR_TAG.

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Acknowledgements

The research reported in this paper was supported by grant 2014-39 from the Swedish Research Council, which funds the Centre for Linguistic Theory and Studies in Probability (CLASP) in the Department of Philosophy, Linguistics, and Theory of Science at the University of Gothenburg. We are grateful to our colleagues in CLASP for helpful discussion of some of the ideas presented here. We also thank the anonymous reviewers and the LACompLing2018 audience for their valuable comments on an earlier draft of the paper.

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  1. Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Box 200, 405 03, Gothenburg, Sweden

    Rasmus Blanck & Aleksandre Maskharashvili

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  1. Rasmus Blanck
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Correspondence to Rasmus Blanck .

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

    Roussanka Loukanova

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Blanck, R., Maskharashvili, A. (2020). From Tree Adjoining Grammars to Higher Order Representations of Abstract Meaning Representations via Abstract Categorial Grammars. 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_4

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