Weighted DAG Automata for Semantic Graphs

Chiang, David; Drewes, Frank; Gildea, Daniel; Lopez, Adam; Satta, Giorgio

doi:10.1162/coli_a_00309

Cited by 17 publications

(34 citation statements)

References 66 publications

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“…Several other types of DAG automata are briefly discussed by Chiang et al (2016). Together with (Quernheim and Knight, 2012;Drewes, 2016, 2017;Drewes, 2017), the latter represents the line of research discussed in this paper.…”

Section: Types Of Dagsmentioning

confidence: 98%

“…3 As discussed by Chiang et al (2016) AMRs should preferably be viewed as multiply-rooted DAGs because their standard representation turns them into singly-rooted graphs only by introduc- 3 We call a vertex a root if it has no incoming edges. ing cycles.…”

Section: Types Of Dagsmentioning

confidence: 99%

“…However, according to statistics reported by Chiang et al (2016), DAGs actually arising from real-world AMRs are usually rather benign. In particular, although the treewidth of AMRs is unbounded in principle, real-world AMRs seem to have a small treewidth.…”

Section: Recognitionmentioning

confidence: 99%

“…The optimal contraction order can be read off an optimal tree decomposition of LG(D). A closer inspection of these facts (Chiang et al, 2016) revels that the algorithm can be implemented to run in time…”

Section: Efficiency Of Recognitionmentioning

confidence: 99%

“…The PropBank frame names (the vertex labels) have been simplified for the sake of readability. They can be found in Chiang et al (2016), which also uses this example. As a side note, one may note that the AMR does not specify whether her saying was the answer to my asking, the other way around, or the two were independent.…”

Section: Introductionmentioning

confidence: 99%

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Proceedings of the 15th Meeting on the Mathematics of Language

Gierasimczuk

Szymanik

2017

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The volume contains eleven regular papers and two invited papers. It also includes an abstract of a third invited talk. The regular papers were selected from a total of 23 submissions, using the EasyChair conference management system. The conference benefited from the financial support of the British Logic Colloquium (http://www. blc-logic.org) and of AYLIEN (http://aylien.com), which we gratefully acknowledge.Last but not least, we would like to express our sincere gratitude to all the reviewers for MOL 2017 and to all the people who helped with the local organization. Partee (1986) claimed without proof that the function BE is the only homomorphism that makes the Partee triangle commute. This paper shows that this claim is incorrect unless "homomorphism" is understood as "complete homomorphism." It also shows that BE and A are the inverses of each other on certain natural assumptions. IntroductionIn a famous and influential paper, Partee (1986) discussed type-shifting operators for NP interpretations, including lift, ident and BE: lift = λxλP. P (x), ident = λxλy. [y = x], BE = λPλx. P(λy. [y = x]).She pointed out that these operators satisfy the equality BE • lift = ident, so the following diagram, now often referred to as the Partee triangle, commutes. Partee declared that BE is "natural" because of the following two "facts." Fact 1. BE is a homomorphism from e, t , t to e, t viewed as Boolean structures, i.e., BE(P 1 P 2 ) = BE(P 1 ) BE(P 2 ), BE(P 1 P 2 ) = BE(P 1 ) BE(P 2 ), BE(¬P 1 ) = ¬BE(P 1 ).Fact 2. BE is the unique homomorphism that makes the diagram commute.While Fact 1 is immediate, Fact 2 is not obvious. Partee (1986) nevertheless did not give a proof of Fact 2, but only a note saying, "Thanks to Johan van Benthem for the fact, which he knows how to prove but I don't." Meanwhile, van Benthem (1986) referred to Partee's work and stated Fact 2 on p. 68, but gave no proof either. Despite this quite obscure exposition, because of the classic status of Partee's and van Benthem's work, I suspect that many linguists take Fact 2 for granted while unable to explain it. Not only is this unfortunate, but it is actually as expected, because Fact 2 turns out to be not quite correct unless "homomorphism" is read as "complete homomorphism." The main purpose of this paper is to rectify this detrimental situation.Van Benthem (1986) took the domain of entities to be finite, writing, "Our general feeling is that natural language requires the use of finite models only" (p. 7). Fact 2 is indeed correct on this assumption. However, natural language has predicates like natural number whose extensions are obviously infinite. Also, if we take the domain of portions of matter in the sense of Link (1983) to be a nonatomic join-semilattice, then the domain of entities will surely be infinite, whether countable or uncountable. It is a fact that a single sentence of natural language, albeit only finitely long, can talk about an infinite number of entities, as exemplified in (1).(1) a. Every natural number is odd or even...

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Section: Types Of Dagsmentioning

confidence: 98%

Section: Types Of Dagsmentioning

confidence: 99%

Section: Recognitionmentioning

confidence: 99%

Section: Efficiency Of Recognitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Proceedings of the 15th Meeting on the Mathematics of Language

Gierasimczuk

Szymanik

2017

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Algorithms and Training for Weighted Multiset Automata and Regular Expressions

DeBenedetto

Chiang

2018

Implementation and Application of Automata

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Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present training methods to learn the weights for weighted regular expressions and for general multiset automata from data. Finally, we examine situations in which inside weights can be computed more efficiently.

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Tree-to-Graph Transductions with Scope

Björklund

2018

Developments in Language Theory

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Weighted DAG Automata for Semantic Graphs

Cited by 17 publications

References 66 publications

Proceedings of the 15th Meeting on the Mathematics of Language

Proceedings of the 15th Meeting on the Mathematics of Language

Algorithms and Training for Weighted Multiset Automata and Regular Expressions

Tree-to-Graph Transductions with Scope

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