A constraint driven metagrammar Joseph Le Roux (1) - Beno e (2) - - - PowerPoint PPT Presentation

A constraint driven metagrammar

Joseph Le Roux(1) - Benoˆ ıt Crabb´ e(2) - Yannick Parmentier(3)

(1) Calligramme Project LORIA - INPL (2) HCRC / ICCS University of Edinburgh (3) Langue Et Dialogue Project INRIA / LORIA - UHP

TAG+8 – Sydney 15 July 2006

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Introduction

◮ Our concern: semi-automatic grammar development of

real-scale Lexicalised TAGs.

◮ Related problems: design and maintnance issues raised by

redundancy inherent to strong lexicalisation.

◮ The MetaGrammar approach:

◮ capturing linguistic generalisations among grammatical

structures (i.e., trees),

◮ describing the trees of a grammar as combinations of

elementary tree fragments.

◮ This work has been realized in collaboration with Pr. Denys

Duchier.

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Outline

eXtensible MetaGrammar Constraining admissible structures An efficient implementation of constraints Some features of the XMG system Conclusion

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eXtensible MetaGrammar (1 / 2)

◮ Monotonic description of the grammar trees using an

expressive and relatively intuitive language.

◮ MetaGrammar ≡ manipulation of elementary tree descriptions

using a control language.

◮ (1) description of tree fragments and (2) combinations of

these fragments.

◮ Two methodological axes of description (Crabb´

e, 05):

• 1. structure sharing (i.e. reusable elementary tree fragments).
• 2. alternatives (i.e. combination of fragments using conjunction

and disjunction).

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eXtensible MetaGrammar (2 / 2)

◮ A language to describe tree fragments:

Description ::= x → y | x →+ y | x →∗ y | x ≺ y | x ≺+ y | x ≺∗ y | x[f :E] | x(p:E) (1)

◮ A language to combine tree fragments:

Class ::= Name → Content (2) Content ::= Description | Name | Content ∨ Content | Content ∧ Content (3)

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Example (1 / 2)

◮ Tree fragment #1:

SubjectCan → (X [cat : s] → Y [cat : v] ) ∧ (X → Z (mark : subst) [cat : n] ) ∧ (Z ≺ Y ) SubjectCan → X [cat:s] Z ↓ [cat:n] Y [cat:v]

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Example (1 / 2)

◮ Tree fragment #1:

SubjectCan → (X [cat : s] → Y [cat : v] ) ∧ (X → Z (mark : subst) [cat : n] ) ∧ (Z ≺ Y ) SubjectCan → X [cat:s] Z ↓ [cat:n] Y [cat:v]

◮ Tree fragment #2:

Active → (X [cat : s] ∧ Y (mark : anchor) [cat : v] ) ∧ X → Y ) Active → X [cat:s] Y ⋄ [cat:v]

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Example (1 / 2)

◮ Tree fragment #1:

SubjectCan → (X [cat : s] → Y [cat : v] ) ∧ (X → Z (mark : subst) [cat : n] ) ∧ (Z ≺ Y ) SubjectCan → X [cat:s] Z ↓ [cat:n] Y [cat:v]

◮ Tree fragment #2:

Active → (X [cat : s] ∧ Y (mark : anchor) [cat : v] ) ∧ X → Y ) Active → X [cat:s] Y ⋄ [cat:v]

◮ Combination rule: Intransitive → SubjectCan ∧ Active (∗)

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Example (2 / 2)

Some trees for intransitive verbs (e.g., the lexical item sleeps)

S N↓ V (Canonical Subject)

∧

S V⋄ (Active verb morph)

⇒

S N↓ V⋄ (e.g. the boy sleeps) N N* S N↓ V (Extracted Subject)

∧

S V⋄ (Active verb morph)

⇒

N N* S N↓ V⋄ (e.g. the boy who sleeps)

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About namespaces

◮ Scope of the node variables used within descriptions ? ◮ local scope by default. ◮ possibility to explicitly manage namespaces via Import /

Export declarations.

◮ Furthermore, introduction of an inheritance mechanism whose

semantics corresponds to class conjunction and namespace merging.

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Outline

eXtensible MetaGrammar Constraining admissible structures An efficient implementation of constraints Some features of the XMG system Conclusion

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Constraining admissible structures

◮ Further constraining the tree structures generated from the

metagrammar.

◮ Specifying constraints on the well-formedness of trees. ◮ Interest: avoid manual checking (e.g. no tree with more than

• ne foot node, etc).

◮ Classification of these constraints into 4 categories:

• 1. Formal constraints
• 2. Operational constraints
• 3. Language-dependent constraints
• 4. Theoretical constraints

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Formal constraints

◮ Constraints assuring that the trees generated by the model

builder are regular TAG trees.

◮ On top of being trees, the output structures must respect

some specific criteria:

◮ each node has a category label, ◮ leaf nodes are either marked as subst, foot or anchor, ◮ the category of the foot node is identical to that of the root

node,

◮ etc. 13 / 32

Operational constraint (1 / 3)

◮ Constraints controlling the combinations of tree fragments

(closely linked to the concept of Resources / Needs).

◮ Constraints based on a colouring of the nodes. ◮ Each node of the description is labelled either Black, Red or

White.

◮ During minimal model computation, nodes are identified

according to the following rules:

• w

+

• w

=

• w
• b

+

• w

=

• b
• b

+

• b

= ⊥

• r

+ { ◦w ;

• b ;
• r}

= ⊥

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Operational constraint (2 / 3)

Benefits:

◮ Avoids node naming issues (no global names). ◮ Allows to reduce the metagrammatical description (node

equations are replaced with implicit coloured node identifications).

◮ Facilitates the reuse of a same tree fragment several times.

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Operational constraint (3 / 3)

Example:

S◦w N•r V◦w (SubjectCan)

∨

N•r N•r S◦w N•r V◦w (SubjectRel)

∧

S•b V⋄•b (Active)

∧

S◦w V◦w N↓•r (ObjectCan) 16 / 32

Language-dependent constraints (1 / 2)

◮ For French, the ordering and uniqueness of clitics. ◮ (Perlmutter, 70):

first they appear in front of the verb in a fixed order according to their rank (a-b) and second two different clitics in front of the verb cannot have the same rank (c).

◮ For instance the clitics le, la have the rank 3 and lui the

rank 4 (rank is a node property). (a) Jean le3 lui4 donne John gives it to him (b) *Jean lui4 le3 donne *John gives to him it (c) *Jean le3 la3 donne *John gives it it

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Language-dependent constraints (2 / 2)

S N↓ V’ ≺+ (Jean)

∧

V’ Cl↓3 V ≺+ (le)

∧

V’ Cl↓4 V ≺+ (lui)

∧

S V’ V⋄ (donne)

⇒

S N↓ V’ Cl↓3 Cl↓4 V⋄ (Jean le lui donne) S N↓ V’ Cl↓4 Cl↓3 V⋄ (Jean lui le donne)

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Theoretical principles

◮ Language-independent principles related to the grammatical

formalism described.

◮ For TAG, such a principle may be the Principle of

Predicate-Argument Coocurrency.

◮ NB: such principles are not yet implemented within the XMG

system.

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Outline

eXtensible MetaGrammar Constraining admissible structures An efficient implementation of constraints Some features of the XMG system Conclusion

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An efficient implementation of constraints

◮ A 3-step metagrammar compilation:

• 1. translation of the descriptions into intermediate code for a

specific virtual machine (WAM-based),

• 2. execution of this code and accumulation of partial tree

descriptions,

• 3. solving of tree descriptions.

◮ The third step is performed by a tree description solver

implemented using the Constraint Satisfaction approach.

◮ In this context, the constraints introduced above can be

expressed naturally.

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Solving Tree Descriptions (1 / 3)

• 1. Setting the constraint framework:

◮ Each node in the input description is associated with an

integer.

◮ Then, we use an asbtract data type to refer to a node of a

valid model in terms of the nodes being equals, above, below,

• r on its side:

Eq Up Down Left Right

Ni

x

::= node( Eq: {ints} Up: {ints} Down: {ints} Left: {ints} Right: {ints})

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Solving Tree Descriptions (2 / 3)

◮ The input description is converted into relation constraints on

node sets. For instance, the dominance relation x → y can be translated as:

Ni

x→ Nj y ≡ [Ni x.EqUp ⊆ Nj y.Up ∧ Ni x.Down ⊇ Nj y.EqDown

∧ Ni

x.Left ⊆ Nj y.Left ∧ Ni x.Right ⊆ Nj y.Right]

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Solving Tree Descriptions (2 / 3)

◮ The input description is converted into relation constraints on

node sets. For instance, the dominance relation x → y can be translated as:

Ni

x→ Nj y ≡ [Ni x.EqUp ⊆ Nj y.Up ∧ Ni x.Down ⊇ Nj y.EqDown

∧ Ni

x.Left ⊆ Nj y.Left ∧ Ni x.Right ⊆ Nj y.Right]

◮

Ni

x.Down ⊇ Nj y.EqDown

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Solving Tree Descriptions (3 / 3)

• 2. Searching the solutions to the problem:

◮ The solutions are the assignments for each of the node sets

associated with the nodes of the input description.

◮ A distribution strategy is used to explore the consistent

assignments for these node sets.

◮ The implementation of the solver follows the ideas of (Duchier

and Niehren, 2000) and uses the constraint programming support of the Oz/Mozart system.

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Extension to specific constraints (1 / 4)

◮ This constraint framework can relatively easily be extended to

solve specific constraints, such as those introduced previously.

◮ The idea:

• 1. extension of the node representation (tuples whose fields

contain sets of nodes),

• 2. definition of additional constraints on these fields, reflecting

the syntactic constraints we want to express.

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Extension to specific constraints (2 / 4)

1st example: Clitic uniqueness.

◮

In a valid model φ, there is only one node having a given property p.

◮ For each node x in the description, we add to its

representation a field containing a boolean variable px indicating whether the node denoting x in the model has this property or not: px ≡ (Ni

x.Eq ∩ Vφ p ) = ∅ ◮ Finally, if true value ∼ 1 and false ∼ 0:

• x∈φ

px ≤ 1

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Extension to specific constraints (3 / 4)

2nd example: Colouring constraint.

◮ During description solving, coloured nodes are identified

according to the following rules:

• w

+

• w

=

• w
• b

+

• w

=

• b
• b

+

• b

= ⊥

• r

+ { ◦w ;

• b ;
• r}

= ⊥

◮ A valid model in this context is a saturated tree, i.e. where

nodes are either black (possibly resulting from identifications)

• r red.

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Extension to specific constraints (4 / 4)

◮ First, the tuples representing nodes are extended by adding a

integer field RB referring to the red or black node with which the node has been identified.

◮ Then, we define the following constraints:

x ∈ VR ⇒ Ni

x.RB = i ∧ Ni x.Eq = {i}

(a) x ∈ VB ⇒ Ni

x.RB = i

(b) x ∈ VW ⇒ Ni

x.RB ∈ Vφ B

(c)

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Outline

eXtensible MetaGrammar Constraining admissible structures An efficient implementation of constraints Some features of the XMG system Conclusion

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Some features of the XMG system

◮ The XMG system has been used successfully to compute a

core TAG for French (6,000+ trees computed from a description containing 293 classes).

◮ This metagrammar has been designed relatively quickly as the

description language is intuitive as advocated in (Crabb´ e, 05).

◮ The compilation of a TAG with more than 6,000 trees takes

about 15 min with a P4 processor 2.6 GHz and 1 GB RAM.

◮ XMG is released under the terms of the GPL-like CeCILL

license and can be freely downloaded at http://sourcesup.cru.fr/xmg

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Conclusion

◮ The XMG formalism includes a fully declarative language. ◮ On top of describing tree-based grammar, XMG allows to

express higher-level constraints such as operational constraints (colours) and language-dependent constraints (Clitic uniqueness).

◮ These specific constraints are processed using Constraint

• Programming. This paradigm allows to extend the library of

constraints easily.

◮ Up to now, the constraints implemented within XMG are:

◮ Colouring. ◮ Uniqueness. ◮ Rank (ordering). ◮ TAG labelling constraints. ◮ Node arity. 32 / 32