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

Stabler - Lx 185/209 2003
3.6.2 Structural relations
(32) Many of the structural properties that linguists look for are expressed as relations among the nodes
in a tree. Here, we make a first pass at defining some of these relations. The following definitions all
identify a node just by its label.
So for example, with the definition just below, we will be able to prove that ip is the root of a tree even
if that tree also contains ip constituents other than the root. We postpone the problem of identifying
nodes uniquely, even when their labels are not unique.
(33) The relation between a tree and its root has a trivial definition:
root(A,A/L).
(34) Now consider the parent relation in trees. Using our notation, it can also be defined very simply, as
follows:
parent(A,B,A/L) :- member(B/_,L).
parent(A,B,_/L) :- member(Tree,L), parent(A,B,Tree).
(35) Domination is the transitive closure of the parent relation. Notice how the following definition avoids
left recursion. And notice that, since no node is a parent of itself, no node dominates itself. Consequently,
we also define dominates_or_eq, which is the reflexive, transitive closure of the parent
relation. Every node, in every tree stands in the dominates_or_eq relation to itself:
dominates(A,B,Tree) :- parent(A,B,Tree).
dominates(A,B,Tree) :- parent(A,C,Tree), dominates(C,B,Tree).
dominates_or_eq(A,A,_).
dominates_or_eq(A,B,Tree) :- dominates(A,B,Tree).
(36) We now define the relation between subtrees and the tree that contains them:
subtree(T/Subtrees,T/Subtrees).
subtree(Subtree,_/Subtrees) :- member(Tree,Subtrees),subtree(Subtree,Tree).
(37) A is a sister of B iff A and B are not the same node, and A and B have the same parent.
Notice that, with this definition, no node is a sister of itself. To implement this idea, we use the important
relation select, whichissortoflikemember, except that it removes a member of a list and
returns the remainder in its third argument. For example, with the following definition, we could prove
select(b,[a,b,c],[a,c]).
sisters(A,B,Tree) :subtree(_/Subtrees,Tree),
select(A/_,Subtrees,Remainder),
member(B/_,Remainder).
select(A,[A|Remainder],Remainder).
select(A,[B|L],[B|Remainder]) :- select(A,L,Remainder).
(38) Various “command” relations play a very important role in recent syntax. Let’s say that A c-commands
B iff A is not equal to B, neither dominates the other, and every node that dominates A dominates B. 16
This is equivalent to the following more useful definition:
16 This definition is similar to the one in Koopman and Sportiche (1991), and to the IDC-command in Barker and Pullum (1990). But
notice that our definition is irreflexive – for us, no node c-commands itself.
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