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Reforming AMR

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Formal Grammar (FG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10686))

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Abstract

Many recent proposals aim to simplify semantic representations, and Abstract Meaning Representation (AMR) comes from this tradition, but it is nevertheless quite expressive. Bos 2016 proposes a slightly reformed AMR for translation to first order logic. This paper proposes a different augmentation of AMR that is more easily provided, and a slightly different mapping to higher order and dynamic logic. The proposed augmentation can be, at least in most cases, easily computed from standard ‘unreformed’ AMR corpora. The mapping from this augmented AMR to logical representation is a finite state multi bottom up tree transduction.

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Notes

  1. 1.

    A tree decomposition of undirected graph g = (V,R) is a tree t = (U,S) where (i) \(\bigcup _{\hbox {u}\in \hbox {U}}\hbox {u}=\hbox {V}\), (ii) if an arc in g connects \(\hbox {v}_i\) and \(\hbox {v}_j\), then some \(\hbox {u}\in \hbox {U}\) contains both \(\hbox {v}_i\) and \(\hbox {v}_j\), and (iii) if some node \(\hbox {v}\) of g is in two nodes \(\hbox {u}_i,\hbox {u}_j\) of U, then \(\hbox {v}\) is in every node on the path between \(\hbox {u}_i\) and \(\hbox {u}_j\). The treewidth of a decomposition is max\(_{\hbox {u}\in \hbox {U}}|\hbox {u}|-1\). The treewidth of g is the minimum treewidth over all decompositions of g. Many problems have complexities that increase with treewidth [7, 20], and Courcelle’s theorem relates treewidth to MSO definability [15]. Computing treewidth is NP-complete, but code for computing treewidth of small graphs is available at [1].

  2. 2.

    HOL with generalized quantifiers is introduced, for example, in Carpenter’s [11, Sect. 3]. Like Carpenter, we write \(\forall x\phi \) for \(\hbox {every}(\lambda x.\phi )\), and \(\exists x\phi \) similarly.

  3. 3.

    The correspondence between AAMR subgraphs and elements of the input string is sometimes given by hand-specified alignments, and there are a number of proposals about how to compute them when hand-specifications are not available [13, 17]. Note that “:polarity -” will be aligned with the negation in the input string. In the example above with ‘most’ and ‘not’, the surface order and the alphanumeric order coincide.

  4. 4.

    The discussion in Hobbs and Shieber has an error that does not affect their main point. Their example sentence is not talking about things that are both representatives and also of-some-company – that doesn’t quite make sense intuitively, and in fact gets the wrong entailments; see e.g. [37]. Rather, representative is relational and of some company specifies one of its arguments. We rephrase the Hobbs and Shieber argument here without that mistake. In the LDC AMR corpus [27], representative is treated relationally as it should be, as denoting an :arg0-of the predicate represent-01, where :arg0 is the representer and :arg1 is the thing represented.

  5. 5.

    Here we focus on the definite article, sketching briefly the fundamental change to a dynamic perspective. But indefinite articles are even trickier and complicate the picture of how scope works, impeding progress until it was recognized that they require special treatment. As discussed for example in Kratzer [28] and references cited there, they are unlike quantifiers like every or three, unlike referential expressions formed with the, and not adequately handled by the discourse closure proposed by Heim [22] and DRT [25]. See e.g. [10].

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Acknowledgments

Many thanks to the anonymous reviewers for their valuable suggestions.

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Authors and Affiliations

  1. University of California, Los Angeles, CA, USA

    Edward Stabler

  2. Nuance Communications, Sunnyvale, CA, USA

    Edward Stabler

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  1. Edward Stabler
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Correspondence to Edward Stabler .

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Editors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Annie Foret

  2. Department of Philosophy, Tilburg University, Tilburg, The Netherlands

    Reinhard Muskens

  3. LORIA/Inria Nancy, Villers-les-Nancy, France

    Sylvain Pogodalla

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Stabler, E. (2018). Reforming AMR. In: Foret, A., Muskens, R., Pogodalla, S. (eds) Formal Grammar . FG 2017. Lecture Notes in Computer Science(), vol 10686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-56343-4_5

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  • DOI: https://doi.org/10.1007/978-3-662-56343-4_5

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