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

Stabler - Lx 185/209 2003
9.2.2 Some CKY-like derivations
(26) The grammar we formulated for the CKY parsing strategy is more succinct than the tree-based formulations,
and most explicitly reveals the insight of Pollard (1984) and Michaelis (1998) that trees play the
role of dividing the input string into a (finite!) number of related parts.
Furthermore, since the latter formulation of the grammar derives tuples of categorized strings, it becomes
feasible to present derivations trees again, since the structures at the derived nodes are tuples
of strings rather than trees.
In fact, the latter representation is succinct enough thatitisfeasibletodisplaymanycompletederivations,
every step in fully explicit form.
With a little practice, it is not difficult to translate back and forth betweeen these explicit derivation trees
and the corresponding X-bar derivations that are more familiar from mainstream linguistic theory. We
briefly survey some examples.
(27) SOVI: Naive Tamil. We first consider some more very simple examples inspired by Mahajan (2000). The
order Subject-Object-Verb-Inflection is defined by the following grammar:
lavinia::d titus::d
praise::vt criticize::vt
laugh::v cry::v
ɛ::=i c -s::=pred +v i
ɛ::=vt =d =d pred -v ɛ::=v =d pred -v
Notice that the -s in the string component of an expression signals that this is an affix, while the -v in
the feature sequence of an expression signals that this item must move to a +v licensing position.
With this lexicon, we have the following derivation of the string titus lavinia praise -s ∈ Sc(NT ):
titus lavinia praise -s: c
ɛ:: =i c titus lavinia praise -s: i
-s: +v i, titus lavinia praise: -v
-s:: =pred +v i titus lavinia praise: pred -v
lavinia praise: =d pred -v
praise:=d=dpred-v
ɛ::=vt=d=dpred-v praise:: vt
lavinia:: d
titus:: d
dP
titus
predP1
dP
lavinia
cP
c iP
predP
pred’
pred vtP
i
-s
praise
These conventional structures show some aspects of the history of the derivations, something which
can be useful for linguists even though it is not necessary for the calculation of derived expressions.
(28) VISO: Naive Zapotec
An VSO language like Zapotec can be obtained by letting the verb select its object and then its subject,
and then moving the just the lowest part of the SOV complex move to the “specifier” of I(nflection). The
following 10 lexical items provide a naive grammar of this kind:
lavinia::d titus::d
praise::vt -v laugh::v -v
ɛ::=i c -s::=pred +v i
ɛ::=vt =d =d pred ɛ::=v =d pred
iP
predP
With this lexicon, we have the following derivation of the string praise -s titus lavinia ∈ Sc(NT ):
188
t1