Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
node with a phonological form with terms of the form Label/–Phon, whereLabel isthenodelabeland
Phon is that node’s phonological form. The tree fragment depicted above is represented by the term
VP/[ DP/ -Mary, V ′
/[ V/-walks, VP/[V ′
/[V/[]]]]].
From a computational perspective, the primary advantage of this representation is that it provides a
simple, structural distinction between (trees consisting of) a node with no phonological content and a
node with no phonological content.
(3) As noted by Gorn (1969), a node can be identified by a sequence of integers representing the choices
made on the path from the root to the node.
We can see how this method works in the following tree, while identifying nodes by their labels does
not:
b[1]
c [1,1]
a[]
b[2]
c [2,1]
(4) Gorn’s path representations of notes are difficult to reason about if the tree is constructed in a non-topdown
fashion, so we consider a another representation is proposed by Hirschman and Dowding (1990)
and modified slightly by Johnson (1991), Johnson and Stabler (1993).
A node is represented by a term
node(Pedigree,Tree,Parent)
where Pedigree is the integer position of the node with respect to its sisters, or else root if the node
is root; Tree is the subtree rooted at this node, and Parent is the representation of the parent node, or
else none if the node is root.
(5) Even though the printed representation of a node can be quadratically larger than the printed representation
of the tree that contains it, it turns out that in most implementations structure-sharing will
occur between subtrees so that the size of a node is linear in the size of the tree.
(6) With this representation scheme, the leftmost leaf of the tree above is represented by the term
n(1,c/[],n(1,b/[c/[]],n(root,a/[b/[c/[]],b/[c/[]]],none)))
(7) With this notation, we can define standard relations on nodes, where the nodes are unambiguously
denoted by our terms:
% child(I, Parent, Child) is true if Child is the Ith child of Parent.
child(I, Parent, n(I,Tree,Parent)) :- Parent = n(_, _/ Trees, _), nth(I, Trees, Tree).
% ancestor(Ancestor, Descendant) is true iff Ancestor dominates Descendant.
% There are two versions of ancestor, one that works from the
% Descendant up to the Ancestor, and the other that works from the
% Ancestor down to the descendant.
ancestor_up(Ancestor, Descendant) :- child(_I, Ancestor, Descendant).
ancestor_up(Ancestor, Descendant) :- child(_I, Parent, Descendant), ancestor_up(Ancestor, Parent).
ancestor_down(Ancestor, Descendant) :- child(_I, Ancestor, Descendant).
ancestor_down(Ancestor, Descendant) :- child(_I, Ancestor, Child), ancestor_down(Child, Descendant).
% root(Node) is true iff Node has no parent
root(n(root,_,none)).
% subtree(Node, Tree) iff Tree is the subtree rooted at Node.
subtree(n(_,Tree,_), Tree).
% label(Node, Label) is true iff Label is the label on Node.
label(n(_,Label/_,_), Label).
% contents(Node, Contents) is true iff Contents is either
% the phonetic content of node or the subtrees of node
contents(n(_,_/Contents,_),Contents).
% children(Parent, Children) is true if the list of Parent’s
% children is Children.
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