Projection

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'''Projection''' is the mechanism by which, in a given syntactic tree, one or two constituents are integrated into a more complex structure. It is the bottom-up movement of merging or collapsing one or two subordinate nodes into a higher node. In the UNL<sup>arium</sup> framework, projection is used to build the sentence structure out of the individual constituents (head, specifier, adjunct and complement) during natural language generation.  
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'''Projection''' is the mechanism by which, in a given syntactic tree, one or two constituents are integrated into a more complex structure. It is the bottom-up movement of merging or collapsing one or two subordinate nodes into a higher node in order to form a [[syntactic structure]]. In the UNL<sup>arium</sup> framework, projection is used to build the sentence structure out of the individual constituents (head, specifier, adjunct and complement) during natural language generation.  
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== Use ==
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Projections are used to build trees out of the head-driven relations, i.e., to go from:
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'''XS(head;specifier);''', which describes the relation between the head of the structure and its specifier
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'''XA(head;adjunct);''', which describes the relation between the head of the structure and its adjuncts
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'''XC(head;complement);''', which describes the relation between the head of the structure and its complements
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'''XH(head);''', which describes the head of the structure
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to:
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<pre>
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    XP
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  / \
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spec  XB
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    / \
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    XB  adjt
 +
  / \
 +
  X  comp
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  |
 +
head
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</pre>
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This is done by a set of rules as follows:
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;first intermediate projection (lower XB)
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XC(%head;%comp):=XB(%head;%comp);
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*projects the first intermediate projection (XB) in case of comp
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XA(%head;%comp):=XB(%head;%adjt);
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*projects the first intermediate projection (XB) in case of adjt (i.e., when there is no comp)
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XH(%head):=XB(%head;);
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*projects the first intermediate projection (XB) when there is no comp or adjt (the second argument is empty)
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;second intermediate projection (if any)
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XB(%head;%xb1)XA(%head;%adjt):=XB(XB(%head;%xb1);%adjt));
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*projects the second intermediate projection (XB) in case of adjt (the tree has a comp or a adjt, or two adjts)
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XB(%head;%comp1)XC(%head;%comp2):=XB(XB(%head;%comp1);%comp2));
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*projects the second intermediate projection (XB) in case of comp (the tree has two comps)
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;third intermediate projection (if any)
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XB(XB(%head;%xb1);%xb2))XA(%head;%adjt):=XB(XB(XB(%head;%xb1);xb2);%adjt)); (the tree has one comp and two adjts, two comps and one adjt or three adjts)
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;fourth intermediate projection (if any)
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...
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;maximal projection
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XB(%head;):=XP(XB(%head;););
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*minimal tree: the tree has only the head (no comp, adjt or spec)
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XB(%head;%xb):=XP(XB(%head;%xb););
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*the tree has only one intermediate projection and no spec
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XB(%head;%xb)XS(%head;%spec):=XP(XB(%head;%xb);%spec);
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*the tree has only one intermediate projection and the spec
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XB(%head;%xb):=XP(XB(%head;%xb););
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*the tree has only one intermediate projection and no spec
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XB(XB(%head;%xb1);%xb2)XS(%head;%spec):=XP(XB(XB(%head;%xb1);%xb2);%spec);
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*the tree has two intermediate projections and the spec
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XB(XB(%head;%xb1);%xb2):=XP(XB(XB(%head;%xb1);%xb2););
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*the tree has two intermediate projections and no spec
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etc.
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XB(XB(%head;%comp);%adjt))XA(%head;%adjt):=
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*projects the third intermediate projection
  
 
== Syntax ==
 
== Syntax ==

Revision as of 21:26, 17 April 2012

Projection is the mechanism by which, in a given syntactic tree, one or two constituents are integrated into a more complex structure. It is the bottom-up movement of merging or collapsing one or two subordinate nodes into a higher node in order to form a syntactic structure. In the UNLarium framework, projection is used to build the sentence structure out of the individual constituents (head, specifier, adjunct and complement) during natural language generation.

Contents

Use

Projections are used to build trees out of the head-driven relations, i.e., to go from: 

XS(head;specifier);, which describes the relation between the head of the structure and its specifier
XA(head;adjunct);, which describes the relation between the head of the structure and its adjuncts
XC(head;complement);, which describes the relation between the head of the structure and its complements
XH(head);, which describes the head of the structure

to: 

    XP
   / \
spec  XB
     / \
    XB  adjt
   / \
  X   comp
  |
head

This is done by a set of rules as follows:

first intermediate projection (lower XB)

XC(%head;%comp):=XB(%head;%comp);

  • projects the first intermediate projection (XB) in case of comp

XA(%head;%comp):=XB(%head;%adjt);

  • projects the first intermediate projection (XB) in case of adjt (i.e., when there is no comp)

XH(%head):=XB(%head;);

  • projects the first intermediate projection (XB) when there is no comp or adjt (the second argument is empty)
second intermediate projection (if any)

XB(%head;%xb1)XA(%head;%adjt):=XB(XB(%head;%xb1);%adjt));

  • projects the second intermediate projection (XB) in case of adjt (the tree has a comp or a adjt, or two adjts)

XB(%head;%comp1)XC(%head;%comp2):=XB(XB(%head;%comp1);%comp2));

  • projects the second intermediate projection (XB) in case of comp (the tree has two comps)
third intermediate projection (if any)

XB(XB(%head;%xb1);%xb2))XA(%head;%adjt):=XB(XB(XB(%head;%xb1);xb2);%adjt)); (the tree has one comp and two adjts, two comps and one adjt or three adjts)

fourth intermediate projection (if any)

...

maximal projection

XB(%head;):=XP(XB(%head;););

  • minimal tree: the tree has only the head (no comp, adjt or spec)

XB(%head;%xb):=XP(XB(%head;%xb););

  • the tree has only one intermediate projection and no spec

XB(%head;%xb)XS(%head;%spec):=XP(XB(%head;%xb);%spec);

  • the tree has only one intermediate projection and the spec

XB(%head;%xb):=XP(XB(%head;%xb););

  • the tree has only one intermediate projection and no spec

XB(XB(%head;%xb1);%xb2)XS(%head;%spec):=XP(XB(XB(%head;%xb1);%xb2);%spec);

  • the tree has two intermediate projections and the spec

XB(XB(%head;%xb1);%xb2):=XP(XB(XB(%head;%xb1);%xb2););

  • the tree has two intermediate projections and no spec

etc.

XB(XB(%head;%comp);%adjt))XA(%head;%adjt):=

  • projects the third intermediate projection

Syntax

Projection rules are S-rules of the replace type, i.e.: 

<RELATION> := <RELATION>;

Where <RELATION> is a syntactic relation, including a <HEAD>, in case of head-only relations (VH, NH, PH, JH, AH, CH, IH, DH), or a <HEAD> and a <ARGUMENT>, in case of binary relations (VC, VS, VA, NC, NS, NA, etc.).

There are mainly two types of projection rules:

  • Replace, when the number of relations in the left side is the same as in the right side, and which is used for collapsing single-branched structures (i.e., parent nodes that have one single child)
  • Merge, when the number of relations in the left side is greater than in the right side, and which is used for collapsing double-branched structures (i.e., parent nodes that have two children).

Examples

  • VH(%head):=VB(%head);
    • The head of the verbal phrase becomes the head of the verbal intermediate projection (VB)
  • VC(%head;%comp):=VB(%head;%comp);
    • The head of the verbal phrase becomes the head of the verbal intermediate projection and the complement of the verbal phrase becomes the second argument of the verbal intermediate projection
  • VB(%head;%comp)VA(%head;%adjt):=VB(VB(%head;%comp);%adjt);
    • The verbal intermediate projection becomes the head of a higher intermediate projection that takes the adjunct to the verb as second argument

Observations

Indexation
As in S-rules, nodes in projection rules are always indexed, either by user-defined labels (such as %head, %comp or any other) or by the position in the left side of the rules.
Sentence structure
The main goal of projection rules is to build the sentence structure described in Syntax.
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