## Regular tree grammars as a formalism for scope underspecification

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Citations: | 3 - 2 self |

### BibTeX

@MISC{Koller_regulartree,

author = {Alexander Koller and Michaela Regneri and Stefan Thater},

title = {Regular tree grammars as a formalism for scope underspecification},

year = {}

}

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### Abstract

We propose the use of regular tree grammars (RTGs) as a formalism for the underspecified processing of scope ambiguities. By applying standard results on RTGs, we obtain a novel algorithm for eliminating equivalent readings and the first efficient algorithm for computing the best reading of a scope ambiguity. We also show how to derive RTGs from more traditional underspecified descriptions.

### Citations

523 |
The Syntactic Process
- Steedman
- 2000
(Show Context)
Citation Context ...proaches to semantic construction which use chart-based packing methods rather than dominance-based underspecification to manage scope ambiguities. For instance, both Combinatory Categorial Grammars (=-=Steedman, 2000-=-) and synchronous grammars (Nesson and Shieber, 2006) represent syntactic and semantic ambiguity as part of the same parse chart. These parse charts can be seen as regular tree grammars that accept th... |

255 |
Minimal recursion semantics: an introduction
- Copestake, Flickinger, et al.
- 2003
(Show Context)
Citation Context ...cient algorithm for computing the best reading of a scope ambiguity. We also show how to derive RTGs from more traditional underspecified descriptions. 1 Introduction Underspecification (Reyle, 1993; =-=Copestake et al., 2005-=-; Bos, 1996; Egg et al., 2001) has become the standard approach to dealing with scope ambiguity in large-scale hand-written grammars (see e.g. Copestake and Flickinger (2000)). The key idea behind und... |

236 |
Tree automata techniques and applications. Available on: http: //www.grappa.univ-lille3.fr/tata
- Comon, Dauchet, et al.
- 1997
(Show Context)
Citation Context ...r costs and then compute a best reading. In this paper, we address both of these shortcomings by proposing regular tree grammars (RTGs) as a novel underspecification formalism. Regular tree grammars (=-=Comon et al., 2007-=-) are a standard approach for specifying sets of trees in theoretical computer science, and are closely related to regular tree transducers as used e.g. in recent work on statistical MT (Knight and Gr... |

177 |
Dealing with ambiguities by underspecification: Construction, representation, and deduction
- Reyle
- 1993
(Show Context)
Citation Context ...he first efficient algorithm for computing the best reading of a scope ambiguity. We also show how to derive RTGs from more traditional underspecified descriptions. 1 Introduction Underspecification (=-=Reyle, 1993-=-; Copestake et al., 2005; Bos, 1996; Egg et al., 2001) has become the standard approach to dealing with scope ambiguity in large-scale hand-written grammars (see e.g. Copestake and Flickinger (2000)).... |

137 | Predicate logic unplugged
- Bos
- 1996
(Show Context)
Citation Context ...uting the best reading of a scope ambiguity. We also show how to derive RTGs from more traditional underspecified descriptions. 1 Introduction Underspecification (Reyle, 1993; Copestake et al., 2005; =-=Bos, 1996-=-; Egg et al., 2001) has become the standard approach to dealing with scope ambiguity in large-scale hand-written grammars (see e.g. Copestake and Flickinger (2000)). The key idea behind underspecifica... |

103 | Training Tree Transducers
- Graehl, Knight, et al.
(Show Context)
Citation Context ...e grammars In order to compute the maximal-weight configuration of a weighted dominance graph, we will first translate it into a weighted regular tree grammar. A weighted regular tree grammar (wRTG) (=-=Graehl and Knight, 2004-=-) is a 5-tuple G = (S,N,Σ,R,c) such 8 that G ′ = (S,N,Σ,R) is a regular tree grammar and c : R → R is a function that assigns each production rule a weight. G accepts the same language of trees as G ′... |

100 | Computational complexity of probabilistic disambiguation by means of tree grammar - Sima’an - 1996 |

91 |
Semirings and their Applications
- Golan
- 1999
(Show Context)
Citation Context ...y scratched the surface of what can be be done with the computation of best configurations in Section 5. The algorithms generalize easily to weights that are taken from an arbitrary ordered semiring (=-=Golan, 1999-=-; Borchardt and Vogler, 2003) and to computing minimal-weight rather than maximal-weight configurations. It is also useful in applications beyond semantic construction, e.g. in discourse parsing (Regn... |

89 | An open source grammar development environment and broad-coverage English grammar using HPSG
- Copestake, Flickinger
- 2000
(Show Context)
Citation Context ...ds style” treebank (Oepen et al., 2002) containing MRS-based underspecified representations for sentences from the tourism domain, and is distributed together with the English Resource Grammar (ERG) (=-=Copestake and Flickinger, 2000-=-). The treebank contains 999 MRS-nets, which we translate automatically into dominance graphs and further into RTGs; the median number of scope readings per sentence is 56. For our experiment, we cons... |

80 | The Constraint Language for Lambda Structures Höche
- Egg, Koller, et al.
- 2001
(Show Context)
Citation Context ...est reading of a scope ambiguity. We also show how to derive RTGs from more traditional underspecified descriptions. 1 Introduction Underspecification (Reyle, 1993; Copestake et al., 2005; Bos, 1996; =-=Egg et al., 2001-=-) has become the standard approach to dealing with scope ambiguity in large-scale hand-written grammars (see e.g. Copestake and Flickinger (2000)). The key idea behind underspecification is that the p... |

68 | The lingo redwoods treebank motivation and preliminary applications
- Oepen, Toutanova, et al.
- 2002
(Show Context)
Citation Context ...he extent to which the new algorithm improves upon KT06, we compare both algorithms on the USRs in the Rondane treebank (version of January 2006). The Rondane treebank is a “Redwoods style” treebank (=-=Oepen et al., 2002-=-) containing MRS-based underspecified representations for sentences from the tourism domain, and is distributed together with the English Resource Grammar (ERG) (Copestake and Flickinger, 2000). The t... |

63 | An Overview of Probabilistic Tree Transducers for Natural Language Processing - Knight, Graehl - 2005 |

37 | An efficient graph algorithm for dominance constraints
- Althaus, Duchier, et al.
(Show Context)
Citation Context ...erceived ambiguity of the sentence. In the past few years, a “standard model” of scope underspecification has emerged: A range of formalisms from Underspecified DRT (Reyle, 1993) to dominance graphs (=-=Althaus et al., 2003-=-) have offered mechanisms to specify the “semantic material” of which the semantic representations are built up, plus dominance or outscoping relations between these building blocks. This has been a v... |

21 |
A Better N-Best List: Practical Determinization of Weighted Finite Tree Automata
- May, Knight
(Show Context)
Citation Context ... are also typically deterministic if the variable names are part of the quantifier node labels. Furthermore, there are algorithms for determinizing weighted tree automata (Borchardt and Vogler, 2003; =-=May and Knight, 2006-=-), which could be applied as preprocessing steps for wRTGs. 6 Conclusion In this paper, we have shown how regular tree grammars can be used as a formalism for scope underspecification, and have exploi... |

16 | Determinization of finite state weighted tree automata - Borchardt, Vogler - 2003 |

16 | Simpler TAG semantics through synchronization
- Nesson, Shieber
- 2006
(Show Context)
Citation Context ...e chart-based packing methods rather than dominance-based underspecification to manage scope ambiguities. For instance, both Combinatory Categorial Grammars (Steedman, 2000) and synchronous grammars (=-=Nesson and Shieber, 2006-=-) represent syntactic and semantic ambiguity as part of the same parse chart. These parse charts can be seen as regular tree grammars that accept the language of parse trees, and conceivably an RTG th... |

11 | 2000. On underspecified processing of dynamic semantics
- Koller, Niehren
(Show Context)
Citation Context ...gle compact underspecified description for each parse. One can then strengthen the underspecified description to efficiently eliminate subsets of readings that were not intended in the given context (=-=Koller and Niehren, 2000-=-; Koller and Thater, 2006); so when the individual readings are eventually computed, the number of remaining readings is much smaller and much closer to the actual perceived ambiguity of the sentence.... |

9 | Formal investigations of underspecified representations - Ebert - 2005 |

9 | A machine learning approach to modeling scope preferences - Higgins, Sadock - 2003 |

6 | The evolution of dominance constraint solvers, in - Koller, Thater - 2005 |

5 | A new well-formedness criterion for semantics debugging
- Flickinger, Koller, et al.
- 2005
(Show Context)
Citation Context ...ets (Niehren and Thater, 2003). The precise definition of dominance nets is not important here, but note that virtually all underspecified descriptions that are produced by current grammars are nets (=-=Flickinger et al., 2005-=-). For the rest of the paper, we restrict ourselves to dominance graphs that are hypernormally connected. 3 Regular tree grammars We will now recall the definition of regular tree grammars and show ho... |

4 | 2006), An improved redundancy elimination algorithm for underspecified representations
- Koller, Thater
(Show Context)
Citation Context ... description for each parse. One can then strengthen the underspecified description to efficiently eliminate subsets of readings that were not intended in the given context (Koller and Niehren, 2000; =-=Koller and Thater, 2006-=-); so when the individual readings are eventually computed, the number of remaining readings is much smaller and much closer to the actual perceived ambiguity of the sentence. In the past few years, a... |

4 |
Skopus und logische Struktur. Studien zum Quantorenskopus im Deutschen
- Pafel
- 1998
(Show Context)
Citation Context ...minance and disjointness edges that are satisfied in t. We can then ask for configurations of maximal weight. Weighted dominance graphs can be used to encode the standard models of scope preferences (=-=Pafel, 1997-=-; Higgins and Sadock, 2003). For example, Higgins and Sadock (2003) present a machine learning approach for determining pairwise preferences as to whether a quantifier Q1 dominates another quantifier ... |

3 | Efficient Processing of Underspecified Discourse Representations - Regneri, Egg, et al. - 2008 |

2 |
Relating dominance formalisms
- Koller, Rambow
- 2007
(Show Context)
Citation Context ...pply equally to dominance-based and chart-based approaches. Indeed, for one particular grammar formalism it has even been shown that the parse chart contains an isomorphic image of a dominance chart (=-=Koller and Rambow, 2007-=-). Finally, we have only scratched the surface of what can be be done with the computation of best configurations in Section 5. The algorithms generalize easily to weights that are taken from an arbit... |

2 |
Efficient solving and exploration of scope ambiguities
- 2005a
(Show Context)
Citation Context ...nd Thater (2006) speculate that further improvements over their (incomplete) redundancy elimination algorithm require a more expressive formalism than dominance graphs. On the theoretical side, Ebert =-=(2005)-=- has shown that none of the major underspecification formalisms are expressively complete, i.e. supports the description of an arbitrary subset of readings. Furthermore, the somewhat implicit nature o... |