Dependency Grammar as Graph Description

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1 Dependency Grammar as Graph Description Ralph Debusmann Programming Systems Lab Universität des Saarlandes Dependency Grammar as Graph Description p.1

2 This talk introduces a new meta grammar formalism for dependency grammar: Extensible Dependency Grammar (XDG) graph description language generalisation of Topological Dependency Grammar (TDG) (Duchier and Debusmann ACL 2001) meta grammar formalism: can be instantiated to yield specific grammar formalisms (including TDG itself) based on dependency grammar Dependency Grammar as Graph Description p.2

3 Dependency grammar collection of ideas for natural language analysis long history (following Kruijff 2002): Greek and Latin scholars: Thrax, Apollonius, and Priscian Indian: Panini s formal grammar of Sanskrit (Astadhyayi/Astaka, 350/250 BC) Arabic: Kitab al-usul of Ibn al-sarrag (d.928) European: Martinus de Dacia (d.1304), Thomas von Erfurt (14th century) modern dependency grammar credited to Tesniere (1959) so what are these ideas? Dependency Grammar as Graph Description p.3

4 Words Bagels, Peter has eaten. Dependency Grammar as Graph Description p.4

5 1:1-correspondence between words and nodes Bagels, Peter has eaten. Dependency Grammar as Graph Description p.5

6 Head/dependent-asymmetry Bagels, Peter has eaten. Dependency Grammar as Graph Description p.6

7 Grammatical functions (edge labels) subj vprt obj Bagels, Peter has eaten. Dependency Grammar as Graph Description p.7

8 Valency (subcategorisation) subj vprt obj Bagels, Peter has { } { } { subj, vprt } eaten. { obj } Dependency Grammar as Graph Description p.8

9 Dependency and phrase structure ideas from dependency grammar adopted by many phrase structure-based grammar formalisms: Government and Binding (GB, Chomsky 1986): X -theory Head-driven Phrase Structure Grammar (HPSG, Pollard and Sag 1994): e.g. DEPS-feature in modern variants (Bouma, Malouf and Sag 1998) Lexical Functional Grammar (LFG, Bresnan and Kaplan 1982): f-structure Tree Adjoining Grammar (TAG, Joshi 1987): derivation tree Dependency Grammar as Graph Description p.9

10 Pure dependency grammar formalisms pure dependency grammar formalisms have been less successful: Abhaengigkeitsgrammatik (Kunze 1975) Functional Generative Description (FGD, Sgall et al 1986) Meaning Text Theory (MTT, Melcuk 1988) Word Grammar (Hudson 1990) why? Dependency Grammar as Graph Description p.10

11 Problems of pure dependency grammar formalisms parsing: no parsers word order: no declarative specification syntax-semantics interface: no compositional semantics construction Dependency Grammar as Graph Description p.11

12 Parsing Duchier (MOL 1999) constraint-based parser for dependency grammar average case efficient (but only small test grammars), although NP-complete in the worst case (Koller and Striegnitz ACL 2002): parser used for LTAG generation, than the generator described in (Carrol et al 1999) (Kuhlmann MSc 2002): parser used for parsing Categorial Type Logics (CTL) Dependency Grammar as Graph Description p.12

13 Word order (Duchier and Debusmann ACL 2001), (Debusmann MSc 2001): Topological Dependency Grammar (TDG) grammar formalism allows declarative specification of word order parsing: Duchier s constraint-based parser Dependency Grammar as Graph Description p.13

14 Syntax-semantics interface goal of my PhD research: develop a syntax-semantics interface for dependency grammar idea: 1. generalise TDG into a metagrammatical framework for dependency grammar (XDG) 2. use XDG to develop the syntax-semantics interface Dependency Grammar as Graph Description p.14

15 Roadmap of the talk 1. XDG basic architecture principles lexicalisation 2. TDG as an instance of XDG 3. syntax-semantics interface Semantic Topological Dependency Grammar (STDG) STDG as another instance of XDG 4. conclusions Dependency Grammar as Graph Description p.15

16 Extensible Dependency Grammar (XDG) graph description language describes a set of graph dimensions a graph dimension is a labeled directed graph G d (V, E d ) all graph dimensions share the same set V of nodes each graph dimension has its own set E d of labeled edges (L d set of edge labels, E d V L d V ) simple feature structures can be attached to each node (features: functions V R, where R is an arbitrary codomain) parametrised principles stipulate well-formedness conditions Dependency Grammar as Graph Description p.16

17 Nodes (arranged in a graph) v 1... v n Dependency Grammar as Graph Description p.17

18 Graph dimensions v 1... v n d m... v 1... v n d 1 Dependency Grammar as Graph Description p.18

19 Feature structures v v n... d m... v v n... d 1 Dependency Grammar as Graph Description p.19

20 Principles P dm v v n... d m... P d1 v v n... d 1 Dependency Grammar as Graph Description p.20

21 Principles (one-dimensional) P dm v v n... d m... P d1 v v n... d 1 Dependency Grammar as Graph Description p.21

22 Principles (multi-dimensional) P dm v v n... d m... P d1 v v n... d 1 Dependency Grammar as Graph Description p.22

23 Principle library directed acyclic graph * tree * in * out * order projectivity climbing barriers linking * covariance and contravariance * node and edge constraints... (extensible) Dependency Grammar as Graph Description p.23

24 Directed acyclic graph dag(g): G is a directed acyclic graph. Dependency Grammar as Graph Description p.24

25 Tree tree(g): G is a tree. Dependency Grammar as Graph Description p.25

26 In out(g d, f): The incoming edges of each node in G d must satisfy the nodes in specification. Feature f : V 2 L d maps an in specification to each node. Dependency Grammar as Graph Description p.26

27 In l 1 v 1 in : { l 1, l 2 } Dependency Grammar as Graph Description p.27

28 In l 2 v 1 in : { l 1, l 2 } Dependency Grammar as Graph Description p.27

29 In in : { l 1, l 2 } Dependency Grammar as Graph Description p.27

30 In l 3 v 1 in : { l 1, l 2 } Dependency Grammar as Graph Description p.27

31 Out out(g d, f): The outgoing edges of each node in G d must satisfy the nodes out specification. Feature f : V (L d 2 N ) maps an out specification to each node. Dependency Grammar as Graph Description p.28

32 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} l 2 l 3 l 3 l 3 Dependency Grammar as Graph Description p.29

33 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} l 2 l 3 l 3 Dependency Grammar as Graph Description p.29

34 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} l 2 l 3 Dependency Grammar as Graph Description p.29

35 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} l 2 Dependency Grammar as Graph Description p.29

36 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} l 2 l 1 Dependency Grammar as Graph Description p.29

37 Out v 1 out : l 1 : {0} l 2 : {1} l 3 : {0,1,2,3} Dependency Grammar as Graph Description p.29

38 Linking linking(g d1, G d2, f): An edge (v 1, l, v 2 ) in G d1 is only licensed if there is a corresponding edge (v 3, l, v 2 ) in G d2, and v 1 links l to l. Feature f : V (L d1 2 L d 2 ) assigns to each node a linking specification. Dependency Grammar as Graph Description p.30

39 Linking d 1 v 1 l link: l : { l } v 2 Dependency Grammar as Graph Description p.31

40 Linking d 1 d 2 link: v 1 l : { l } l v 3 v 2 v 2 Dependency Grammar as Graph Description p.31

41 Linking d 1 d 2 link: v 1 l : { l } l v 3 l v 2 v 2 Dependency Grammar as Graph Description p.31

42 Linking d 1 d 2 v 1 l v 3 l link: l : { l } v 2 v 2 Dependency Grammar as Graph Description p.31

43 Linking d 1 d 2 v 1 l link: l : { l } v 2 v 2 Dependency Grammar as Graph Description p.31

44 Covariance covariance(g d1, G d2, f): Each edge (v 1, l, v 2 ) in G d1 where l is covariant on v 1 is only licensed if v 1 is above v 2 in G d2. Feature f : V 2 L d 1 assigns to each node its set of covariant labels. Dependency Grammar as Graph Description p.32

45 Covariance d 1 v 1 l co : { l } v 2 Dependency Grammar as Graph Description p.33

46 Covariance d 1 d 2 v 1 co : { l } l v1 v 2 v2 Dependency Grammar as Graph Description p.33

47 Covariance d 1 d 2 v 1 co : { l } l v 2 v 2 v 1 Dependency Grammar as Graph Description p.33

48 Contravariance contravariance(g d1, G d2, f): Each edge (v 1, l, v 2 ) in G d1 where l is contravariant on v 1 is only licensed if v 1 is below v 2 in G d2. Feature f : V 2 L d 1 assigns to each node its set of contravariant labels. Dependency Grammar as Graph Description p.34

49 Lexicalisation 1. from dependency grammar: 1:1-correspondence between nodes and words 2. assign to each word a set of lexical entries (feature structures) 3. select one of the lexical entries, efficient through selection constraint (Duchier MOL 1999) 4. assign the selected entry (feature structure) to the corresponding node Dependency Grammar as Graph Description p.35

50 XDG architecture so far P dm v v n... d m... P d1 v v n... d 1 Dependency Grammar as Graph Description p.36

51 Words P dm v v n... d m... P d1 v v n... d 1 w 1 w n Dependency Grammar as Graph Description p.37

52 Lexical entries P dm v v n... d m... P d1 v v n... d 1 w 1 w n Dependency Grammar as Graph Description p.38

53 Selection P dm v v n... d m... P d1 v v n... d 1 w 1 w n Dependency Grammar as Graph Description p.39

54 Lexical assignment P dm v v n... d m... P d1 v v n... d 1 w 1 w n Dependency Grammar as Graph Description p.40

55 XDG instantiation recipe for getting XDG instances: 1. define graph dimensions 2. define used principles and parameters Dependency Grammar as Graph Description p.41

56 XDG does TDG two graph dimensions: G ID and G LP ID dimension: Immediate Dominance; edge labels: grammatical functions like subj, obj (subject, object) LP dimension: Linear Precedence; edge labels: topological fields (linear positions) like topf, subjf (topicalisation field, subject field) Dependency Grammar as Graph Description p.42

57 Principles used on the ID dimension tree(g ID ) in(g ID, in ID ) out(g ID, out ID ) nodeconstraints(...) edgeconstraints(g ID, f) Dependency Grammar as Graph Description p.43

58 Principles used on the LP dimension tree(g LP ) in(g LP, in LP ) out(g LP, out LP ) order(g LP,..., on) projectivity(g LP ) climbing(g ID, G LP ) barriers(g ID, G LP, blocks) Dependency Grammar as Graph Description p.44

59 TDG analysis subj vinf obj ID A woman, every man seems to love. Dependency Grammar as Graph Description p.45

60 TDG analysis topf subjf vcf LP A woman, every man seems to love. subj vinf obj ID A woman, every man seems to love. Dependency Grammar as Graph Description p.45

61 Syntax-semantics interface Semantic Topological Dependency Grammar (STDG) new grammar formalism, extends TDG with a syntax-semantics interface to underspecified semantics underspecification formalism: Constraint Language for Lambda Structures (CLLS, Egg, Niehren, Ruhrberg, Xu 1998) other target semantics formalisms possible Dependency Grammar as Graph Description p.46

62 Constraint Language for Lambda Structures (CLLS) CLLS based on dominance constraints (Marcus/Hindle/Fleck 1983) CLLS structures describe λ-terms example: A woman, every man seems to love. scopally ambiguous: strong and weak reading (quantifier order: and ) Dependency Grammar as Graph Description p.47

63 lam lam every seem var love var Dependency Grammar as Graph Description p.48

64 lam lam a seem var love var Dependency Grammar as Graph Description p.49

65 XDG does STDG four graph dimensions: G ID, G LP, G TH, G DE ID and LP dimensions as in TDG TH dimension: THematic dag; edge labels: semantic roles like act, pat (actor, patient) DE dimension: CLLS DErivation tree; edge labels: CLLS fragment positions like r, s (restriction, scope) Dependency Grammar as Graph Description p.50

66 Principles used on the TH dimension dag(g TH ) in(g TH, in TH ) out(g TH, out TH ) linking(g TH, G ID, link) Dependency Grammar as Graph Description p.51

67 Principles used on the DE dimension tree(g DE ) in(g DE, in DE ) out(g DE, out DE ) covariance(g DE, G TH, co) contravariance(g DE, G TH, contra) Dependency Grammar as Graph Description p.52

68 STDG analysis LP topf subjf vcf A woman, every man seems to love. subj vinf obj A woman, every man seems to love. ID Dependency Grammar as Graph Description p.53

69 STDG analysis LP topf subjf vcf A woman, every man seems to love. subj vinf prop obj pat act A woman, every man seems to love. A woman, every man seems to love. ID TH Dependency Grammar as Graph Description p.54

70 STDG analysis (strong reading) LP DE topf subjf vcf s s s A woman, every man seems to love. A woman, every man seems to love. subj vinf prop obj pat act A woman, every man seems to love. A woman, every man seems to love. ID TH Dependency Grammar as Graph Description p.55

71 STDG analysis (weak reading) LP DE topf subjf vcf s s s A woman, every man seems to love. A woman, every man seems to love. subj vinf prop obj pat act A woman, every man seems to love. A woman, every man seems to love. ID TH Dependency Grammar as Graph Description p.56

72 From STDG to CLLS lexicon: words correspond to CLLS fragments (subtrees) STDG analysis contains all information to build a CLLS representation of the semantics: DE tree: assembly of fragments/scope TH dag: lambda bindings Dependency Grammar as Graph Description p.57

73 Words correspond to lam a A woman, every man seems to love. man seem var love var CLLS Dependency Grammar as Graph Description p.58

74 DE tree: assembly of fragments DE s lam a A woman, every man seems to lam every seem var love var CLLS Dependency Grammar as Graph Description p.59

75 TH dag: lambda bindings DE s lam a A woman, every man seems to lam every prop pat act var var A woman, every man seems to love. TH CLLS Dependency Grammar as Graph Description p.60

76 TH dag: lambda bindings DE s lam a A woman, every man seems to lam every prop pat act var var A woman, every man seems to love. TH CLLS Dependency Grammar as Graph Description p.61

77 Summary dependency grammar appealing but pure dependency grammar approaches flawed (Duchier MOL 99) solves the parsing problem TDG (Duchier and Debusmann ACL 2001), (Debusmann MSc 2001) solves the word order problem but still no syntax-semantics interface generalised TDG to XDG TDG as an instance of XDG syntax-semantics interface: developed STDG as another instance of XDG Dependency Grammar as Graph Description p.62

78 State of the art proof of concept: STDG syntax-semantics interface works for small example grammar new XDG parser (as efficient as the TDG parser) new XDG parser system (statically typed frontend, XML support) demo Dependency Grammar as Graph Description p.63

79 Related work interface to information structure (Duchier and Kruijff EACL 2003) grammar induction (Korthals and Kruijff 2003) (Korthals MSc 2003) Stochastic Extensible Dependency Grammar (SXDG) (Dienes, Koller and Kuhlmann PASSI 2003) Dependency Grammar as Graph Description p.64

80 XDG people a number of people are involved in XDG: Lille: Joachim Niehren Nancy: Denys Duchier Saarbrücken: Ondrej Bojar, Peter Dienes, Alexander Koller, Christian Korthals, Geert-Jan Kruijff, Marco Kuhlmann, Mathias Möhl, Stefan Thater Dependency Grammar as Graph Description p.65

81 Outlook integration of preferences (for e.g. PP attachment, scope) search for equivalences between instances of XDG and existing grammar formalisms (find e.g. context-free and mildly context-sensitive XDG instances) Tree Insertion Grammar (TIG, Schabes and Waters 1993) TAG (Joshi 1987) CCG (Steedman 2000), MMCCG (Baldridge and Kruijff 2003) development of bigger grammars: handcrafted induced (Penn Treebank, TIGER, Prague Dependency Treebank) ported (XTAG) Dependency Grammar as Graph Description p.66

82 Thank you! Any questions? Dependency Grammar as Graph Description p.67

An Improved Redundancy Elimination Algorithm for Underspecified Representations

An Improved Redundancy Elimination Algorithm for Underspecified Representations Alexander Koller and Stefan Thater Dept. of Computational Linguistics Universität des Saarlandes, Saarbrücken, Germany {koller,stth}@coli.uni-sb.de