Head-driven Phrase Structure Grammar I
Head-driven Phrase Structure Grammar I Head-driven Phrase Structure Grammar I
Head-driven Phrase Structure Grammar I Weiwei Sun Institute of Computer Science and Technology Peking University May 10, 2013
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<strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I<br />
Weiwei Sun<br />
Institute of Computer Science and Technology<br />
Peking University<br />
May 10, 2013
Basic Idea Typed feature structure HPSG: First glance<br />
Lexicalized grammar formalism<br />
◮ Linguistic rules to derive syntactic structures are mainly<br />
introduced by lexical entries, which are structures assigned to<br />
words.<br />
◮ A number of modern syntactic theories fall into lexicalized<br />
grammars:<br />
◮ Lexicalized tree-adjoining grammar (last lecture)<br />
◮ <strong>Head</strong>-<strong>driven</strong> phrase structure grammar (this lecture)<br />
◮ Lexical functional grammar<br />
◮ Combinatory categorial grammar<br />
◮ Lexicalized grammars provides a mathematical framework for<br />
describing linguistic structures.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 2/61
Basic Idea Typed feature structure HPSG: First glance<br />
Outline<br />
Basic Idea<br />
Typed feature structure<br />
HPSG: First glance<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 3/61
Basic Idea Typed feature structure HPSG: First glance<br />
Motivation<br />
CFG treats each grammatical category symbol as atomic without<br />
internal structure.<br />
⇒ Two categories are either identical or different.<br />
⇒ There is no mechanism for saying that two categories are alike<br />
in some ways, but different in others.<br />
Words and phrases in NLs typically behave alike in certain<br />
respects, but not others.<br />
Cross-cutting grammatical properties<br />
3rd singular subject plural subject<br />
direct object NP denies deny<br />
No direct object NP disappears disappear<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 3/61
Basic Idea Typed feature structure HPSG: First glance<br />
Features and values<br />
◮ Linguistic feature: a property-like element that indicates<br />
the grammatical behavior of syntactic constituents.<br />
◮ The elements associated to linguistic expressions, such as<br />
words, can be broken down.<br />
◮ Features are usually modeled as pairs of feature names and<br />
feature values.<br />
Feature Example Value<br />
person I go, you go, he goes 1st, 2nd, 3rd<br />
number he dances, they dance singular, plural<br />
case he brings Bob, Bob brings him nominative accusative<br />
tense go, went, gone past, present, future<br />
modality may, can, conditional, subjunctive<br />
A nice summary of linguistic features<br />
http://www.grammaticalfeatures.net<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 4/61
Basic Idea Typed feature structure HPSG: First glance<br />
Features and values<br />
◮ Whereas NPs, VPs, NNs, etc. are conceived of as<br />
categories (first-class “citizens”) in the grammar, features<br />
are more property-like.<br />
◮ Features are conceived of as the atomic units that<br />
compose more complex categories.<br />
◮ The VP has the feature value past tense.<br />
◮ The verb is a past tense verb.<br />
◮ The noun has a case feature accusative.<br />
A noun is a feature set of semantic, morphological and phonological<br />
features:<br />
⎡<br />
form<br />
⎢<br />
⎣number<br />
animacy<br />
⎤<br />
dog<br />
⎥<br />
singular ⎦<br />
animate<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 5/61
Basic Idea Typed feature structure HPSG: First glance<br />
Feature structure<br />
◮ Use a feature structure to specify of grammatical information.<br />
◮ Formally, a feature structure is a specification of a set of<br />
features, each of which is paired with a particular value.<br />
Descriptions<br />
Feature structures can be<br />
represented by a type of<br />
attribute-value matrix (AVM).<br />
⎡<br />
⎤<br />
FEATURE 1 VALUE 1<br />
FEATURE 2 VALUE 2<br />
⎢<br />
⎣...<br />
⎥<br />
⎦<br />
FEATURE n VALUE n<br />
Example<br />
〈 [ ]〉<br />
pos noun<br />
bird,<br />
num singular<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 6/61
Basic Idea Typed feature structure HPSG: First glance<br />
More on feature values<br />
Atomic value<br />
An unstructured value, one with only one part<br />
[<br />
tense<br />
]<br />
past<br />
person 2<br />
Complex value<br />
A structured value, itself a feature structure<br />
⎡<br />
tense<br />
⎢<br />
⎣agreement<br />
⎤<br />
past<br />
[ ]<br />
person 2 ⎥<br />
⎦<br />
number singular<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 7/61
Basic Idea Typed feature structure HPSG: First glance<br />
Handling valence with a feature<br />
IV, TV and DTV<br />
IV: TV: DTV:<br />
[ ]<br />
pos verb<br />
[ ]<br />
pos verb<br />
[ ]<br />
pos verb<br />
word<br />
val<br />
itr<br />
word<br />
val<br />
tr<br />
word<br />
val<br />
dtr<br />
V<br />
]<br />
V=<br />
[pos verb<br />
word<br />
N, NP<br />
N: NP:<br />
[<br />
pos<br />
word<br />
]<br />
noun<br />
[<br />
pos<br />
phrase<br />
]<br />
noun<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 8/61
Basic Idea Typed feature structure HPSG: First glance<br />
Handling valence with a feature<br />
VP→V NP ∗<br />
⎡ ⎤<br />
] word<br />
⎢ ⎥<br />
→ ⎣pos 1 ⎦<br />
pos 1<br />
val itr<br />
b. [ ⎡ ⎤<br />
] word<br />
phrase<br />
[<br />
⎢ ⎥<br />
→ ⎣pos 1 ⎦ pos<br />
pos 1<br />
val tv<br />
c. [ ⎡ ⎤<br />
] word<br />
phrase<br />
[<br />
⎢ ⎥<br />
→ ⎣pos 1 ⎦ pos<br />
pos 1<br />
val dtv<br />
(1) a. [ phrase<br />
]<br />
noun<br />
][<br />
noun pos<br />
]<br />
noun<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 9/61
Basic Idea Typed feature structure HPSG: First glance<br />
Handling agreement with a feature<br />
S→NP VP<br />
(2) S →<br />
[<br />
pos<br />
]<br />
noun<br />
num 1<br />
phrase<br />
[<br />
pos<br />
]<br />
verb<br />
num 1<br />
phrase<br />
With valence<br />
⎡<br />
⎤<br />
◮ [ ] pos noun<br />
pos noun ⎢<br />
⎥<br />
→ ⎣num 1 ⎦<br />
num 1<br />
phrase<br />
val itr<br />
word<br />
⎡<br />
⎤<br />
◮ [ ] pos noun<br />
pos noun ⎢<br />
⎥<br />
→ ⎣num 1 ⎦NP<br />
num 1<br />
phrase<br />
val tr<br />
phrase<br />
⎡<br />
⎤<br />
◮ [ ] pos noun<br />
pos noun ⎢<br />
⎥<br />
→ ⎣num 1 ⎦NP NP<br />
num 1<br />
phrase<br />
val tr<br />
phrase<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 10/61
Basic Idea Typed feature structure HPSG: First glance<br />
HPSG: Assumptions<br />
Two assumptions<br />
1. Languages are systems of sorts of linguistic objects at<br />
avariety of levels of abstraction.<br />
◮ <strong>Grammar</strong>s assign structural descriptions and semantic<br />
interpretations to linguistic objects.<br />
2. <strong>Grammar</strong>s are best represented as process-neutral systems<br />
of declarative constraints.<br />
◮ TG defines contraints in terms of operations on objects<br />
(movements).<br />
◮ TAG defines contraints in terms of adjunctions.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 11/61
Basic Idea Typed feature structure HPSG: First glance<br />
Developing a feature structure based syntactic theory<br />
Questions<br />
Define feature structures in a linguistic way<br />
◮ What kinds of features go together<br />
◮ What values are appropriate for each particular feature<br />
Manipulate feature structures in a systematic way<br />
◮ How to specify which feature structures are well-formed<br />
◮ How to combine small feature structures to larger ones<br />
Mathematically sound model is employed to guarantee that rich<br />
features can be widely defined for modeling various linguistic<br />
phenomena.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 12/61
Basic Idea Typed feature structure HPSG: First glance<br />
Developing a feature structure based syntactic theory<br />
Type ⇒ Typed feature structure<br />
◮ One of the first things in developing a theory of grammars<br />
is to classify linguistic entities.<br />
◮ Paradigmatic relations: We cluster “good” feature<br />
structures into various types.<br />
◮ Syntagmatic relations: We combine “good” feature<br />
structures according to several general principles.<br />
◮ HPSG employs Typed feature structure (TFS), a<br />
mathematical device, to express symbolic and structured<br />
constraints of linguistic objects.<br />
1. Types are associated with feature-value constraints<br />
expressed as TFS’s.<br />
2. Linguistic objects “of the same type” share its<br />
feature-value constraints.<br />
3. A concrete linguistic object may define other feature-value<br />
constraints, which are compatible with its type.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 13/61
Basic Idea Typed feature structure HPSG: First glance<br />
Reference<br />
HPSG is a syntactic theory that follows the lexicalist framework.<br />
1. (Sag and Wasow, 1999) ⇒ (Sag, Wasow and Bender<br />
2003):<br />
◮ Syntactic Theory: A Formal Introduction<br />
2. (Pollard and Sag, 1994):<br />
◮ <strong>Head</strong>-Driven <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong><br />
HPSG describes linguistic structures with typed feature structures<br />
◮ (Carpenter, 1992):<br />
◮ The Logic of Typed Feature <strong>Structure</strong>s<br />
◮ (Copestake, 2000):<br />
◮ Appendix: Definitions of typed feature structures.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 14/61
Basic Idea Typed feature structure HPSG: First glance<br />
Outline<br />
Basic Idea<br />
Typed feature structure<br />
HPSG: First glance<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 15/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Informal idea<br />
A type hierarchy<br />
◮ states what kinds of objects we claim exist (the types)<br />
◮ organizes the objects hierarchically into classes with shared<br />
properties (the type hierarchy)<br />
◮ states what general properties each kind of object has (the<br />
feature and feature value declarations).<br />
◮ describes a classification of feature structures.<br />
⇒ It classifies the corresponding linguistic objects modeled by the<br />
feature structures.<br />
Types are occasionally referred to as sorts.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 15/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Informal idea<br />
Multiple inheritance allows classification on multiple dimensions<br />
◮ In the CFG way, strings are classified in only one dimension.<br />
What do these CFG categories have in common<br />
NP VP are both phrases<br />
N V are both words<br />
NP N are both ‘nouny’<br />
VP V are both ‘verby’<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 16/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Informal idea<br />
Multiple inheritance allows classification on multiple dimensions<br />
◮ In the CFG way, strings are classified in only one dimension.<br />
What do these CFG categories have in common<br />
NP VP N V<br />
NP VP are both phrases<br />
N V are both words<br />
NP N are both ‘nouny’<br />
VP V are both ‘verby’<br />
phrase word nouny verby<br />
sign<br />
func<br />
⊥<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 16/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Informal idea<br />
Given two types σ, τ, we usually want to talk about:<br />
◮ σ is more general than τ<br />
◮ τ is more specific than σ<br />
◮ σ is a supertype of τ<br />
◮ τ is a subtype of σ<br />
◮ One unique type subsumes all other types<br />
◮ Types without any subtype are called maximal types.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 17/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Subsumption<br />
◮ T : is a finite set of types<br />
◮ ⊑: a partial order defined on T<br />
◮ Reflexive: σ ⊑ σ<br />
◮ Antisymmetric: if σ ⊑ τ and τ ⊑ σ then σ = τ<br />
◮ Transitive: if σ ⊑ ω and ω ⊑ τ then σ ⊑ τ<br />
◮ Subsumption: For types σ, τ ∈ T , σ subsumes or is more<br />
general than or is a supertype of τ, when σ ⊑ τ.<br />
◮ τ is subsumed by or is more specific than or is a subtype of σ.<br />
Example<br />
dolphin elephant salmon<br />
aquatic-animal terrestrial-animal mammal fish<br />
animal<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 18/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Most general common subtype of two types<br />
Definition<br />
◮ For types τ 1 , τ 2 ∈ T , τ 1 and τ 2 are consistent if they have<br />
a common subtype or an upper bound σ ′ , such that<br />
τ 1 ⊑ σ ′ and τ 2 ⊑ σ ′ .<br />
◮ A least upper bound σ (lub(τ 1 , τ 2 )) of τ 1 and τ 2 is defined<br />
as follows:<br />
◮ σ is an upper bound of τ 1 and τ 2 .<br />
◮ For any upper bound σ ′ of τ 1 and τ 2 , σ ⊑ σ ′ .<br />
dolphin elephan salmon<br />
aquatic-animal terrestrial-animal mammal fish<br />
animal<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 19/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type hierarchy: Formal definition<br />
A type system consists of a type hierarchy plus a set of constraints<br />
which determine which typed feature structures are well-formed.<br />
Definition<br />
Type hierarchy H is a pair 〈T , ⊑〉 that satisfies the following<br />
condition: For all τ 1 , τ 2 ∈ T ,<br />
◮ lub(τ 1 , τ 2 ) = ∅ or<br />
◮ there exist one unique σ, such that lub(τ 1 , τ 2 ) = {σ}.<br />
We denote the most general type in a type hierarchy by ⊥.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 20/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type unification: Definition<br />
Definition<br />
Unification of types τ 1 , τ 2 ∈ T is an operation to compute the<br />
least upper bound of τ 1 and τ 2 . Type unification of τ 1 and τ 2 if<br />
denoted by τ 1 ⊔ τ 2 . That is,<br />
{ σ if lub(τ1 , τ<br />
τ 1 ⊔ τ 2 =<br />
2 ) = {σ}<br />
undefined otherwise<br />
dolphin elephan salmon<br />
aquatic-animal terrestrial-animal mammal fish<br />
animal<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 21/61
Basic Idea Typed feature structure HPSG: First glance<br />
Typed feature structure: Informal Idea<br />
<br />
<br />
<br />
<br />
<br />
<br />
◮ TFS’s can be represented as rooted directed labeled graphs:<br />
◮ Nodes are labeled with types<br />
◮ Edges are labeled with features.<br />
◮ A feature path is a list of features through a feature structure<br />
leading to a particular value.<br />
◮ Reentrancy/structure-sharing: two attributes denote identical<br />
information.<br />
Example<br />
predicate<br />
subj<br />
P RED<br />
noun<br />
verb<br />
AGR<br />
agreement<br />
P ERS<br />
AGR<br />
NUM<br />
3rd<br />
singular<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 22/61
Basic Idea Typed feature structure HPSG: First glance<br />
Attribute-Value Matrix (AVM)<br />
Attribute-value matrix (AVM) notation is a description language to<br />
describe sets of feature structures, with the following three building<br />
blocks:<br />
◮ Type descriptions selects all objects of a particular type.<br />
◮ Attribute-value pairs describe objects that have a particular<br />
property.<br />
◮ The attribute must be appropriate for the particular type, and<br />
the value can be any kind of description<br />
◮ Tags to specify token identity<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 23/61
Basic Idea Typed feature structure HPSG: First glance<br />
AVM: An example<br />
Type, attribute-value pairs and tags.<br />
Example<br />
⎡ 〈 〉<br />
⎤<br />
phon she<br />
⎡<br />
⎡ ⎡<br />
[<br />
] ⎤<br />
⎤<br />
head<br />
case nom<br />
noun<br />
⎡ ⎤<br />
cat<br />
subj 〈〉<br />
⎢<br />
⎢ ⎥<br />
valence<br />
⎣<br />
⎣comps 〈〉 ⎦ ⎥<br />
⎦<br />
spr 〈〉<br />
cat<br />
val<br />
⎡<br />
⎡<br />
⎤⎤<br />
ss<br />
per 3rd<br />
loc<br />
⎢<br />
⎥<br />
index 1 ⎣num<br />
sing⎦<br />
cont<br />
⎢<br />
gend fem ⎥<br />
⎣<br />
ref<br />
⎦<br />
restr {}<br />
ppro<br />
⎡<br />
⎧ [ ]⎫ ⎤<br />
⎨<br />
⎢<br />
⎢ ⎢<br />
reln female ⎬ ⎢ ⎣<br />
⎣conx<br />
⎣bkgr<br />
⎩ inst 1<br />
⎭<br />
⎦<br />
⎦⎥<br />
⎣<br />
psoa ⎦<br />
synsem<br />
local<br />
context<br />
word<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 24/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS: Graphs or AVMs<br />
<br />
<br />
<br />
<br />
<br />
<br />
Graph<br />
noun<br />
3rd<br />
predicate<br />
SUBJ<br />
AGR<br />
agreement<br />
P ERS<br />
P RED<br />
verb<br />
AGR<br />
NUM<br />
singular<br />
AVM<br />
⎡<br />
⎡<br />
[ ]⎤ ⎤<br />
person 3rd<br />
subj ⎣agr 1<br />
⎦<br />
num singular<br />
agreement<br />
⎢ noun<br />
⎣<br />
]<br />
⎥<br />
⎦<br />
pred<br />
[agr 1<br />
verb<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 25/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS: Formal definition<br />
Definition<br />
A typed feature structure is defined on a finite set of features F<br />
and a type hierarchy 〈T , ⊑〉. It is a tuple 〈Q, r, δ, θ〉, where:<br />
◮ Q is a finite set of nodes<br />
◮ r ∈ Q (r is the root node)<br />
◮ δ : Q × F ↦→ Q is a partial feature value function<br />
◮ θ : Q ↦→ T is a partial typing function<br />
subject to the following conditions:<br />
1. r isn’t a δ-descendant.<br />
2. all members of Q except r are δ-descendants of r.<br />
(*) there is no node n or path π such that δ(n, π) = n.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 26/61
Basic Idea Typed feature structure HPSG: First glance<br />
Reentrancy: Informal Idea<br />
Question<br />
Shouldn’t a person live together with his/her spouse<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 27/61
Basic Idea Typed feature structure HPSG: First glance<br />
Reentrancy: Informal Idea<br />
<br />
<br />
<br />
<br />
<br />
<br />
◮ Reentrant structure: one in which the attribute has a value<br />
that is another feature structure.<br />
◮ Reentrancy is also called token identity or path equivalence<br />
predicate<br />
SUBJ<br />
P RED<br />
noun<br />
verb<br />
AGR<br />
agreement<br />
P ERS<br />
AGR<br />
NUM<br />
3rd<br />
singular<br />
<strong>Structure</strong> sharing<br />
The main explanatory mechanism in HPSG is that of structuresharing,<br />
equating two features as having the exact same value.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 28/61
Basic Idea Typed feature structure HPSG: First glance<br />
Reentrancy: Informal Idea<br />
Agreement and valence<br />
◮ S →<br />
[ ]<br />
pos noun<br />
[ ]<br />
pos verb<br />
num 1<br />
num 1<br />
phrase<br />
phrase<br />
⎡ ⎤<br />
◮ [ ] pos verb<br />
pos verb ⎢ ⎥<br />
→ ⎣num 1 ⎦<br />
num 1<br />
phrase<br />
val itr<br />
word<br />
⎡ ⎤<br />
◮ [ ] pos verb<br />
pos verb ⎢ ⎥<br />
→ ⎣num 1 ⎦NP<br />
num 1<br />
phrase<br />
val tr<br />
phrase<br />
⎡ ⎤<br />
◮ [ ] pos verb<br />
pos verb ⎢ ⎥<br />
→ ⎣num 1 ⎦NP NP<br />
num 1<br />
phrase<br />
val tr<br />
phrase<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 29/61
Basic Idea Typed feature structure HPSG: First glance<br />
Reentrancy: Formal Definition<br />
◮ A path is understood as a sequence of features: π ∈ F + .<br />
◮ δ(n, π) is the value node starting from n following path π.<br />
Definition<br />
If δ(r, π) = δ(r, π ′ ) and π = π ′ , i.e. two paths start from the<br />
root of the feature structure and point to the same node, then<br />
it is said there is a reentrancy between path π and π ′<br />
Feature path<br />
⎡<br />
⎡<br />
[ ]⎤ ⎤<br />
person 3rd<br />
subj ⎣agr 1<br />
⎦<br />
num singular<br />
agreement<br />
⎢ noun<br />
⎣<br />
]<br />
⎥<br />
⎦<br />
pred<br />
[agr 1<br />
verb<br />
Path: 〈SUBJ, AGR, NUM 〉 = singular<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 30/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS subsumption: Informal idea<br />
Subsumption between feature structures:<br />
◮ A less specific (more abstract) feature structure subsumes<br />
an equally or more specific one.<br />
The subsumption symbol: ⊑.<br />
Example<br />
[<br />
[ ] ⎡<br />
⎤<br />
◮ number PL]<br />
⊑ number PL ⊑ number PL<br />
⎢<br />
⎥<br />
person 3 ⎣person 3 ⎦<br />
phon dog<br />
[ ] [<br />
]<br />
◮ number PL ¬ ⊑ number PL<br />
person 3<br />
[<br />
] [<br />
]<br />
◮ number PL ¬ ⊑ number SG<br />
]<br />
◮ [] ⊑<br />
[number SG<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 31/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS subsumption: Formal definition<br />
◮ π ≡ F π ′ : feature structure F contains path equivalence or<br />
reentrancy between the paths π and π ′<br />
Definition<br />
◮ δ(r, π) = δ(r, π ′ ) where r is the root node of F.<br />
F subsumes F ′ , written F ⊑ F ′ , if and only if:<br />
◮ π ≡ F π ′ implies π ≡ F ′ π ′<br />
◮ θ(δ(r, π)) = σ implies θ(δ(r ′ , π)) = σ ′ and σ ⊑ σ ′ .<br />
In other words, feature structure F subsumes feature structure F ′<br />
(F ⊑ F ′ ) iff:<br />
1. if path π is defined in F then π is also defined in F ′ and the<br />
type of the value of π in F is a supertype or equal to the type<br />
of the value of π in F ′ , and<br />
2. all paths that are reentrant in F are also reentrant in F ′ .<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 32/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: Informal idea<br />
◮ Unification is a binary operation over two features<br />
structures F and F ′ , used for comparing or combining<br />
information.<br />
◮ Unification of F and F ′ either returns<br />
◮ a merged feature structure with the information from both<br />
F and F ′ ,<br />
◮ or false if F and F ′ are incompatible.<br />
◮ The unification symbol is ⊔.<br />
Example<br />
[<br />
◮ number<br />
[<br />
◮ number<br />
◮ [ number<br />
]<br />
PL ⊔<br />
[<br />
number<br />
] [<br />
PL ⊔ number<br />
] [<br />
]<br />
PL ⊔ person 2 =<br />
] [<br />
PL = number<br />
]<br />
SG = False<br />
[ ]<br />
number PL<br />
person 2<br />
]<br />
PL<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 33/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: Informal idea<br />
◮ Decide whether two typed feature structures are mutually<br />
compatible;<br />
◮ determine combination of two TFS’s to give the most general<br />
feature structure which retains all information which they<br />
individually contain;<br />
◮ if there is no such feature structure, unification fails;<br />
◮ unification monotonically combines information from both<br />
“input” TFS’s;<br />
◮ relation to subsumption: the unification of two structures F<br />
and F ′ is the most general TFS which is subsumed by both F<br />
and F ′ (if it exists).<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 34/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: Formal definition (skip)<br />
Definition<br />
Suppose F, F ′ ∈ FS such that F = 〈Q, r, θ, δ〉, F ′ =<br />
〈Q ′ , r ′ , θ ′ , δ ′ 〉, and Q ∩ Q ′ = ∅. We first define an equivalence<br />
relation ⊲⊳ on Q ∪ Q ′ as the least equivalence relation such that:<br />
◮ r ⊲⊳ r ′<br />
◮ δ(f, q) ⊲⊳ δ(f, q ′ ) if both are defined and r ⊲⊳ r ′<br />
The unification of F and F ′ is defined as:<br />
F ⊔ F ′ = 〈(Q ∪ Q ′ )/ ⊲⊳ , [r] ⊲⊳ , θ ⊲⊳ , δ ⊲⊳ 〉<br />
where: θ ⊲⊳ ([q] ⊲⊳ ) = ∪{(θ ∪ θ ′ )(q ′ )|q ′ ⊲⊳ q} and<br />
⎧<br />
⎨ [(δ ∪ δ ′ )(f, q)] ⊲⊳ if (δ ∪ δ ′ )(f, q) is a well<br />
δ ⊲⊳ (f, [q] ⊲⊳ ) =<br />
defined function<br />
⎩<br />
undefined otherwise<br />
Similarly, [(δ ∪ δ ′ )(f, q)] ⊲⊳ denotes ∪{〈q ′ , (δ ∪ δ ′ )(q ′ )〉|q ′ ⊲⊳ q}.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 35/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (1)<br />
q 1 AGR q 2 P ERS q 3<br />
q 0<br />
SUBJ<br />
q 6<br />
P RED<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
q 7<br />
◮ Q = {q 0 , q 1 , q 2 , q 3 , q 4 , q 5 , q 6 , q 7 }<br />
◮ r = q 0<br />
◮ θ = {q 0 → predicate, q 1 → noun, q 2 → agreement, q 3 →<br />
3rd, q 4 → verb, q 5 → agreement, q 6 → 3rd, q 7 →<br />
singular}<br />
◮ δ = {(SUBJ, q 0 ) → q 1 , (P RED, q 0 ) → q 4 , (AGR, q 1 ) →<br />
q 2 , (P ERS, q 2 ) → q 3 , (AGR, q 4 ) → q 5 , (P ERS, q 5 ) →<br />
q 6 , (NUM, q 5 ) → q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 36/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (2)<br />
<br />
<br />
SUBJ<br />
q ′ 1<br />
AGR<br />
<br />
q ′ 0<br />
P RED<br />
<br />
AGR<br />
q ′ 2<br />
q ′ 3<br />
◮ Q ′ = {q ′ 0 , q′ 1 , q′ 2 , q′ 3 }<br />
◮ r ′ = q ′ 0<br />
◮ θ ′ = {q 0 → predicate, q 1 → noun, q 2 → agreement, q 3 →<br />
verb}<br />
◮ δ ′ = {(SUBJ, q ′ 0 ) → q′ 1 , (P RED, q′ 0 ) → q′ 3 , (AGR, q 1) →<br />
q 2 , (AGR, q 3 ) → q 2 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 37/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (3)<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
q 0<br />
SUBJ<br />
P RED<br />
q 1 AGR q 2 P ERS q 3<br />
q 1<br />
′<br />
SUBJ<br />
q 6 q 0<br />
′<br />
P ERS<br />
q 4 AGR q 5 NUM <br />
P RED<br />
q 7 <br />
q ′ 3<br />
AGR<br />
<br />
q 2<br />
′<br />
AGR<br />
{q 1 , q 1 ′ }<br />
SUBJ<br />
AGR P ERS<br />
<br />
{q 0 , q 0 ′ } {q 2 , q 5 , q 2 ′ }<br />
P RED NUM<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 3 , q ′ 6 }<br />
{q 7 }<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 38/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: An example (4)<br />
{q 3 , q ′ 6 }<br />
{q 0 , q ′ 0 } SUBJ<br />
P RED<br />
<br />
{q 1 , q ′ 1 } AGR<br />
<br />
{q 4 , q ′ 3 } AGR<br />
{q 2 , q 5 , q ′ 2 } P ERS<br />
NUM<br />
{q 7 }<br />
◮ (Q ∪ Q ′ )/ ⊲⊳ = {{q 0 , q ′ 0 }, {q 1, q ′ 1 }, {q 4, q ′ 3 }, {q 2, q 5 , q ′ 2 }, {q 3, q 6 }, {q 7 }}<br />
◮ [r] ⊲⊳ = {q 0 , q ′ 0 }<br />
◮ θ = {{q 0 , q ′ 0 } → predicate, {q 1, q ′ 1 } → noun, {q 4, q ′ 3 } →<br />
verb, {q 2 , q 5 , q ′ 2 } → agreement, {q 3, q 6 } → 3rd, {q 7 } → singular}<br />
◮ δ = {(SUBJ, {q 0 , q ′ 0 }) → {q 1, q ′ 1 }, (P RED, {q 0, q ′ 0 }) →<br />
{q 4 , q ′ 3 }, (AGR, {q 1, q ′ 1 }) → {q 2, q 5 , q ′ 2 }, (P ERS, {q 2, q 5 , q ′ 2 }) →<br />
{q 3 , q 6 }, (AGR, {q 4 , q ′ 3 }) → {q 2, q 5 , q ′ 2 }, (NUM, {q 2, q 5 , q ′ 2 }) → {q 7}<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 39/61
Basic Idea Typed feature structure HPSG: First glance<br />
Unification: More examples<br />
Example<br />
◮<br />
[<br />
agreement<br />
[<br />
⎡<br />
[<br />
⎣ agreement number<br />
number PL<br />
number PL] ] ⊔ [ number PL]<br />
=<br />
] ⎤<br />
PL<br />
⎦<br />
Example<br />
t 3 t 4<br />
t 1 t 2<br />
⊥<br />
1.<br />
2.<br />
3.<br />
[ ]<br />
[<br />
F1 t 2<br />
F 1 t 1<br />
]⊔<br />
=<br />
t 4 F 2 t 3<br />
t 4<br />
[ ] [ ]<br />
F1 t 1 F1 1<br />
⊔<br />
=<br />
F 2 t 2 F 2 1<br />
t 4 ⊥<br />
[ ] [ ]<br />
F1 1 t 1 F2 1<br />
⊔<br />
F 2 1 F 3 1 t 4<br />
⊥<br />
⊥<br />
[ ]<br />
F1 t 3<br />
F 2 t 3<br />
t 4<br />
[ ]<br />
F1 1<br />
F 2 1 t 3<br />
t 4<br />
= False<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 40/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS for linguistic description<br />
How should I model linguistic objects by FEATURES<br />
In practice,<br />
◮ The grammar specifies partial descriptions of type constraints,<br />
which are automatically expanded to give constraint<br />
structures which meet the conditions given.<br />
◮ Once a type system is defined, specifications of rules and<br />
lexical entries are expanded so that they are well-formed<br />
according to the type system.<br />
Question<br />
Why so many Greek symbols<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 41/61
Basic Idea Typed feature structure HPSG: First glance<br />
A real-world ontology of linguistic objects<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 42/61
Basic Idea Typed feature structure HPSG: First glance<br />
TFS for linguistic description: An example<br />
Example<br />
⎡ 〈 〉<br />
⎤<br />
phon she<br />
⎡<br />
⎡ ⎡<br />
[<br />
] ⎤<br />
⎤<br />
head<br />
case nom<br />
noun<br />
⎡ ⎤<br />
cat<br />
subj 〈〉<br />
⎢<br />
⎢ ⎥<br />
valence<br />
⎣<br />
⎣comps 〈〉 ⎦ ⎥<br />
⎦<br />
spr 〈〉<br />
cat<br />
val<br />
⎡<br />
⎡<br />
⎤⎤<br />
ss<br />
per 3rd<br />
loc<br />
⎢<br />
⎥<br />
index 1 ⎣num<br />
sing⎦<br />
cont<br />
⎢<br />
gend fem ⎥<br />
⎣<br />
ref<br />
⎦<br />
restr {}<br />
ppro<br />
⎡<br />
⎧ [ ]⎫ ⎤<br />
⎨<br />
⎢<br />
⎢ ⎢<br />
reln female ⎬ ⎢ ⎣<br />
⎣conx<br />
⎣bkgr<br />
⎩ inst 1<br />
⎭<br />
⎦<br />
⎦⎥<br />
⎣<br />
psoa ⎦<br />
synsem<br />
local<br />
context<br />
word<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 43/61
Basic Idea Typed feature structure HPSG: First glance<br />
Appropriateness of feature structures: Motivated idea<br />
Pollard and Sag (1994: 8) require the HPSG architecture to use<br />
TFS as models of linguistic objects. They assume the underlying<br />
mathematical models to be totally well-typed and sort-resolved<br />
feature structures.<br />
Totally well-typedness<br />
◮ What attribute labels can appear in a feature structure is<br />
determined by its sort.<br />
◮ Every feature that is appropriate for the sort assigned to<br />
that node is actually present.<br />
Sort-resolvedness<br />
◮ Every node is assigned a most specific type as value.<br />
◮ Types that do not subsume any other sorts (except for<br />
themselves) are called maximally specific types/sorts.<br />
◮ A type is a disjunction of its maximally specific subtypes.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 44/61
Basic Idea Typed feature structure HPSG: First glance<br />
Sort-resolvedness<br />
◮ The idea: Linguistic objects are entities of maximally specific<br />
sorts whose components are again of maximally specific sorts.<br />
∗ Sort-resolvedness is not a necessary property of feature<br />
structures.<br />
An example drawn from (Pollard and Sag, 1994)<br />
◮ word and phrase<br />
◮ are immediate subsorts of sign and<br />
◮ have no proper subsorts.<br />
◮ We can talk about signs with AVMs, but in the real world<br />
◮ we only find feature structures of the maximally specific<br />
sorts word or phrase;<br />
◮ there is no such thing as a feature structure of type sign<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 45/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type constraints and appropriate features: Informal idea<br />
◮ Well-formed TFS’s satisfy all type constraints from the<br />
type hierarchy.<br />
◮ Type constraints are typed feature structures associated<br />
with a type.<br />
◮ The top-level features of a type constraint are appropriate<br />
features.<br />
◮ Type constraints express generalizations over a “class”<br />
(set) of objects.<br />
Type Constraint Appropriate features<br />
*ne-list*<br />
] FIRST, REST<br />
[<br />
first ⊥<br />
*ne-list*<br />
rest<br />
*list*<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 46/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type constraints and appropriate features: Formal stuff (skip)<br />
Types are associated with constraints expressed as TFS’s.<br />
◮ Constraint function C : T ↦→ FS<br />
◮ Define conditions on the constraint function.<br />
◮ For each type there is a set of features appropriate to that<br />
type<br />
AppFeat : T ↦→ F<br />
Definition<br />
◮ Feat(F, q) is defined to be the set of features labeling<br />
transitions from the node q in some feature structure F<br />
i.e. f ∈ Feat(F, q) such that δ(f, q) is defined.<br />
◮ If C(t) = 〈Q, r, δ, θ〉, then the appropriate features of t are<br />
defined as Appfeat(t) = Feat(F, r).<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 47/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type constraints and appropriate features: Formal stuff (skip)<br />
Definition: Well-formed feature structures<br />
F = 〈Q, r, δ, θ〉 is a well-formed feature structure if and only if<br />
for all q ∈ Q, we have that<br />
1. C(θ(q)) ⊑ F ′ = 〈Q ′ , q, δ, θ〉<br />
2. Feat(F, q) = Appfeat(θ(q)).<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 48/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type constraints and appropriate features: Formal stuff (skip)<br />
Constraint function C : T ↦→ FS obeys the following conditions:<br />
1. Type For a given type t, if C(t) is the feature structure<br />
〈Q, r, δ, θ〉 then θ(r) = t.<br />
2. Monotonicity Given type t 1 and t 2 , if t 1 ⊑ t 2 then<br />
C(t 1 ) ⊑ C(t 2 ).<br />
3. Compatibility of constraints For all q ∈ Q the feature<br />
structure C(θ(q)) ⊑ F ′ = 〈Q ′ , q, δ, θ〉 and<br />
Feat(q) = Appfeat(θ(q))<br />
4. Maximal introduction of features For every feature<br />
f ∈ Feat there is a unique type t such that f ∈ Appfeat(t)<br />
and there is no type s such that s ⊏ t and f ∈ Appfeat(s).<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 49/61
Basic Idea Typed feature structure HPSG: First glance<br />
Type inference: Making a TFS well-formed<br />
◮ Apply all type constraints to convert a TFS into a well-formed<br />
TFS.<br />
◮ Determine most general well-formed TFS subsumed by the<br />
input TFS;<br />
◮ Specialize all types so that all features are appropriate:<br />
[ ] [ ]<br />
head pos head pos<br />
→<br />
args *list*<br />
args *list*<br />
⊥<br />
phrase<br />
◮ Expand all nodes with the type constraint of the type of that<br />
node:<br />
[ ]<br />
head pos<br />
→<br />
args *list*<br />
phrase<br />
⎡<br />
head<br />
args<br />
⎢<br />
⎣spr<br />
comps<br />
phrase<br />
⎤<br />
pos<br />
*list*<br />
*list*<br />
⎥<br />
⎦<br />
*list*<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 50/61
Basic Idea Typed feature structure HPSG: First glance<br />
Outline<br />
Basic Idea<br />
Typed feature structure<br />
HPSG: First glance<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 51/61
Basic Idea Typed feature structure HPSG: First glance<br />
Signature<br />
A signature consists of<br />
◮ A type inheritance hierarchy 〈T , ⊑〉.<br />
◮ A corresponding constraint function C : 〈T , ⊑〉 ↦→ FS.<br />
◮ FS: a collection of TFS’s.<br />
◮ Appropriate features and constraints on types<br />
◮ Linguistic theories are developed by describing the inheritance<br />
type hierarchy together with proper constraints<br />
⇒ A constraint-based grammar framework.<br />
Linguistic objects are modeled by feature structures, they are<br />
total with respect to the ontology declared in the signature.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 51/61
Basic Idea Typed feature structure HPSG: First glance<br />
Signature<br />
These feature structures are<br />
◮ Totally well-formed: every node has all the features<br />
appropriate for its type and each attribute has an appropriate<br />
value<br />
◮ Type-resolved: every node is of a maximally specific type<br />
◮ Sometimes partially described: underspecifying information<br />
Linguistic description<br />
◮ Linguistic theories are described using AVMs.<br />
◮ A set of description statements comprises the constraints:<br />
◮ What are the admissible linguistic objects<br />
⇔ there is a corresponding well-formed TFS satisfying all<br />
the constraints<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 52/61
Basic Idea Typed feature structure HPSG: First glance<br />
Linguistic description<br />
Example<br />
(3) a. Ja spal. I masc.sg slept masc.sg<br />
b. On spal. He masc.sg slept masc.sg<br />
⎡<br />
⎡<br />
⎢<br />
⎣synsem | loc<br />
word<br />
cat | head<br />
⎢<br />
⎣cont | index<br />
⎤<br />
noun<br />
[ ]<br />
num 3<br />
⎥<br />
⎦<br />
gen masc<br />
This AVM specifies the “partial” constraints on the complete<br />
(totally well-typed) feature structure of the subject.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 53/61
Basic Idea Typed feature structure HPSG: First glance<br />
Feature structures in HPSG<br />
◮ HPSG is nonderivational, but in some sense, HPSG has<br />
several different levels (layers of features)<br />
◮ Each of these feature values is itself a complex object.<br />
Signs in HPSG<br />
Sign is the basic sort/type in HPSG used to describe lexical items<br />
(of type word) and phrases (of type phrase).<br />
◮ The type sign has the features PHON and SYNSEM.<br />
◮ The feature SYNSEM has a value of type synsem<br />
◮ This type itself has relevant features (LOCAL and<br />
NONLOCAL)<br />
◮ ...<br />
sign<br />
⎡<br />
phon<br />
⎢<br />
⎣synsem<br />
⎤<br />
list(phone-string)<br />
[ ]<br />
local local ⎥<br />
⎦<br />
nonlocal nonlocal<br />
synsem<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 54/61
Basic Idea Typed feature structure HPSG: First glance<br />
Feature structures in HPSG<br />
◮ local introduces CAT(cateogry), CONT(content) and<br />
CONX(context)<br />
◮ non-local is connected with unbounded dependencies<br />
◮ category includes,<br />
◮ The sign’s syntactic category<br />
◮ Given via the feature [HEAD head], where head is the<br />
supertype for noun, verb, adjective, preposition, determiner,<br />
marker<br />
◮ each of these types selects a particular set of head features<br />
◮ The sign’s subcategorzation frame/valence.<br />
◮<br />
⎡Three list-valued features<br />
⎤<br />
⎡<br />
⎤<br />
subj list(synsem)<br />
⎢<br />
⎢<br />
⎥<br />
⎣<br />
synsem | loc | cat | valence ⎣spec<br />
list(synsem) ⎦⎥<br />
⎦<br />
comps list(synsem)<br />
valuence<br />
◮ If any of these lists are non-empty, the sign has the potential<br />
to combine with another sign<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 55/61
Basic Idea Typed feature structure HPSG: First glance<br />
Feature structures in HPSG<br />
Example<br />
⎡ 〈 〉<br />
⎤<br />
phon she<br />
⎡<br />
⎡ ⎡<br />
[<br />
] ⎤ ⎤⎤<br />
head<br />
case nom<br />
noun<br />
⎡ ⎤<br />
cat<br />
subj 〈〉<br />
⎢<br />
⎢ ⎥<br />
⎣valence<br />
⎣comps 〈〉 ⎦<br />
⎥<br />
⎦<br />
spr 〈〉<br />
cat<br />
val<br />
⎡<br />
⎡<br />
⎤<br />
ss<br />
per 3rd<br />
loc<br />
⎢<br />
index 1 ⎣num<br />
sing⎦<br />
cont<br />
⎢<br />
gend fem ⎥<br />
⎣<br />
ref<br />
⎦<br />
restr {}<br />
ppro<br />
⎡<br />
⎧ [<br />
]⎫ ⎤<br />
⎨<br />
⎢ ⎢ ⎢<br />
reln female ⎬ ⎢ ⎣ ⎣conx<br />
⎥<br />
⎣bkgr<br />
⎣<br />
⎩ inst 1<br />
⎦<br />
⎭ ⎦⎥<br />
psoa ⎦<br />
synsem local context<br />
word<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 56/61
Basic Idea Typed feature structure HPSG: First glance<br />
The building blocks of HPSG<br />
From a linguistic perspective, an HPSG consists of<br />
1. A lexicon: licensing basic words<br />
2. Lexical rules: licensing derived words<br />
3. Immediate dominance (ID) schemata: licensing<br />
constituent structure<br />
4. Linear precedence (LP) statements: constraining word<br />
order<br />
5. Grammatical principles: expressing generalizations about<br />
linguistic objects<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 57/61
Basic Idea Typed feature structure HPSG: First glance<br />
The lexicon<br />
◮ The basic lexicon defines the ontologically possible words that<br />
are grammatical:<br />
word → lexical entry1 ∨ lexical entry2 ∨ ...<br />
◮ Each lexical entry is described by an AVM.<br />
Example<br />
◮ Ja/On spal. I masc.sg /He masc.sg slept masc.sg<br />
spal v1 le<br />
⎡<br />
phon<br />
ss | loc<br />
⎢<br />
⎣<br />
〈 〉<br />
spal<br />
⎡ ⎡<br />
]<br />
head<br />
[vform fin<br />
⎡ verb cat<br />
〈<br />
⎢<br />
⎣val<br />
⎣ subj comps 〈〉<br />
⎢<br />
⎣<br />
[<br />
]<br />
cont sleeper 1<br />
sleep<br />
′<br />
NP[NOM] 1 [misc,sing]<br />
⎤<br />
⎤⎤<br />
〉 ⎤<br />
⎥<br />
⎦<br />
⎥<br />
⎦<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 58/61
Basic Idea Typed feature structure HPSG: First glance<br />
Types of phrases<br />
◮ Each phrase has a DTRS attribute which has a<br />
constituent-structure value<br />
◮ This DTRS value corresponds to what we view in a tree as<br />
daughters (with additional grammatical role information, e.g.<br />
adjunct, complement, etc.)<br />
◮ By distinguishing different kinds of constituent-structures, we<br />
can define different kinds of constructions in a language<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 59/61
Basic Idea Typed feature structure HPSG: First glance<br />
Types of phrases<br />
Example<br />
⎡<br />
〈<br />
〉 ⎤<br />
phon she, drinks, wine<br />
⎡<br />
⎤<br />
head 3<br />
[ ]<br />
ss | loc | cat ⎢<br />
⎣ subj 〈〉 ⎥<br />
⎢<br />
val<br />
⎦<br />
⎣<br />
comps 〈〉 ⎥<br />
⎦<br />
DTRS head-subj-struc<br />
S<br />
H<br />
⎡ 〈 〉 ⎤<br />
⎣ phon she<br />
⎦<br />
ss 1<br />
⎡<br />
phon<br />
ss | loc | cat<br />
⎢<br />
⎣<br />
⎡<br />
〈<br />
〉 ⎤<br />
phon drinks, wine<br />
⎡<br />
⎤<br />
head 3<br />
⎡ 〈 〉 ⎤<br />
ss | loc | cat ⎢<br />
⎣val<br />
⎣ subj 1 ⎥<br />
⎦<br />
⎢<br />
⎣<br />
comps 〈〉 ⎥<br />
⎦<br />
DTRS<br />
H<br />
head-comps-struc<br />
〈 〉<br />
⎤<br />
drinks<br />
⎡<br />
[<br />
]<br />
⎤<br />
head 3 vform fin<br />
verb<br />
⎡<br />
〈 〉 ⎤<br />
subj 1<br />
⎢ ⎢<br />
⎥<br />
⎣val<br />
⎣ 〈 〉<br />
⎦<br />
⎥<br />
⎦<br />
comps 2<br />
C<br />
⎡ 〈 〉 ⎤<br />
⎣ phon wine<br />
⎦<br />
ss 2<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 60/61
Basic Idea Typed feature structure HPSG: First glance<br />
LingGO grammar<br />
◮ LinGO = Linguistic <strong>Grammar</strong> Online<br />
◮ http://lingo.stanford.edu/<br />
◮ Research focus: Development of<br />
◮ linguistically precise grammars based on the HPSG framework,<br />
◮ general-purpose tools for use in grammar engineering, profiling,<br />
parsing and generation.<br />
◮ English Resource <strong>Grammar</strong>:<br />
◮ The LinGO grammar consists of a specification of a type<br />
system and of various TFS’s which are well-formed according<br />
to the type system.<br />
◮ The TFS’s function as grammar rules, lexical rules and lexical<br />
entries.<br />
Weiwei Sun <strong>Head</strong>-<strong>driven</strong> <strong>Phrase</strong> <strong>Structure</strong> <strong>Grammar</strong> I 61/61