Transcript Lecture 10

CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSGs
Unification
review, HPSG
Introduction,
Principles,
Rules,
Examples,
Modularity
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Unification Review
Robinson 1965
all formulae represented in disjunctive normal form
namely,
p1 ^ . . . pk  q1  . . .  qt
is equivalent to:
¬p1  . . .¬pk  q1  . . .  qt
three inference rules:
1. resolution
2. substitution
3. simplification
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Unification Review: Inference Rules
Specialization (substitution):
 x/t
replace a variable x by term t
Resolution:
from → p   and   p →  resolve to    →   
Simplification:
p  p   →  becomes p   → 
 →   p  p becomes  →   p
and some others.
This inference system is sound and refutation complete; i.e., if
a set of facts is inconsistent then we can derive the
contradiction: T
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Unification Review: Examples
As usual, x and y are variables and a and b are
constants.
UNIF(on(a,x), on(a, b)) = x → b
UNIF(on(a,x), on(y, b)) = x → b, y → a
UNIF(on(a,x), on(y, f(y ))) = y → a, x → f(a)
UNIF(on(x, y ), on(y, f(y ))) = fail
UNIF(on(a,x), on(x, b)) = fail(a  b)
UNIF( f(x, g(y, y),x), f(z,z, g(w, f(T))) ) = ?
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
HPSG was developed by Carl Pollard and Ivan Sag
since 1987, initially as a refinement and extension
of Generalized Phrase Structure Grammars
(Gazdar, 1981) and belongs to a family of phrase
structure-theoretic approaches in which a rich set of
lexical specifications, coupled with a few very
general combinatorial constraints and restrictions
on information sharing, interact monotonically to
give rise to sets of complex objects called feature
structures, which model the properties of linguistic
signs.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
Consider, for example, an auxilliary verb in English. Such
verbs select a certain class of subjects and appear either in
canonically ordered sentences (Robin has left) or inverted
sentences (Has Robin left?). In HPSG such a linguistic
expression will be modled by a feature structure including a
specification for the feature CAT, provided relevant syntactic
information, including specification of the HEAD properties of
that expression - those which are invariably shared
betweenmother and head daughter. The feature HEAD is then
taken to be a function which maps a particular node labeled
by the sort category to a particular node of sort noun, verb,
and so on; for verbs, this latter node itself is mapped by a
function VFORM to a node labeled by one of a set of sorts
fin(ite), inf(inite), … by a function AUX to one of the sorts …
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
A long-standing, near-universal, and erroneous practice of
teaching syntax in a void exists, as if the communicative
function of language had nothing to do with syntax. And
semantics has customarily been taught in sequence after
syntax, or else not at all. ... [ HPSG ] seeks to redress this
situation by building up syntactic and semantic aspects of
grammatical theory in an integrated way from the start, under
the assumption that neither is of linguistic interest divorced
from the other.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
The theory presented, head-driven phrase structure grammar - so
called because of its central notion of the grammatical head - is an
information-based (or unification-based) theory that has roots in
different research programs within linguistics and neighboring
disciplines (philosophy and computer science). HPSG draws upon
and attempts to synthesize theories, such as categorial grammar,
lexical-functional grammar, generalized phrase-structure grammar,
and government-binding theory; but many key ideas arise from
semantic theories like situation semantics and discourse
representation theory, and from computational work in knowledge
representation, data type theory, and formalisms based on the
unification of partial information.
...Carl Pollard, 1987
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
HPSG is not a theory of syntax. Researchers into GB, GPSG,
and LFG have focused on syntax, relying mainly on a Montaguestyle system of model-theoretic interpretation. In contrast, HPSG
theory inextricably intertwines syntax and semantics, that is,
syntactic and semantic aspects of grammatical theory are built up
in an integrated way from the start. Thus HPSG is closer in spirit
to situation semantics, and this closeness is reflected in the
choice of ontological categories in terms of which the semantic
contents of signs are analyzed: individuals, relations, roles,
situations and circumstances.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
9
CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Driven Phrase Structure Grammars (HPSGs)
HPSG is an information-based theory of natural language syntax
and semantics. It was developed by synthesizing a number of
theories mentioned above. In these theories syntactic features
are classified as head features, binding features and the
subcategorization feature; thus HPSG uses three principles of
universal grammar including:
Head Feature Principle
Binding Inheritance Principle
Subcategorization Principle
Instructor: Nick Cercone - 3050 CSEB - [email protected]
10
CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Head Feature Principle
Similar to GPSG’s Head Feature Convention. It states
that head features (e.g., part of speech, the case of
nouns, verb inflection) of a phrasal sign be shared with
its head daughter, e.g., case of a noun phrase is
determined by the case of its head noun, etc.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Binding Inheritance Principle
Similar to GPSG’s Foot Feature Principle. Binding
features encode syntactic dependencies of signs that
are essentially nonlocal such as the presence of gaps,
relative pronouns, etc. This principle states that
dependency information be transmitted up the sign’s
constituent structure until the dependency can become
“bound/saturated”.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Subcategorization Principle
Generalization of categorial grammar’s “argument cancellation”.
Subcategorization is described by a SUBCAT feature. SUBCAT
value is a list of signs with which the sign in question must combine
to be saturated. For example, the SUBCAT value of the past-tense
intransitive verb walked is the list NP [NOM] since walked must
combine with a single nominative case NP (the subject) to be
saturated; past tense transitive verb liked has the SUBCAT value
NP[ACC], NP[NOM] since liked requires accusative-case NP
(direct object) & nominative-case NP (subject).
• Dowty, D. (1982a), Grammatical Relations and Montague Grammar. in P. Jacobson and
G. K. Pullam (eds) The Nature of Syntactic Represenations. Dordrecht, Riedel.
• Dowty, D. (1982b), More on the Categorial Analysis of Grammatical Relations. in A.
Zaenen (ed) Subjects and Other Subjects: Proceedings of the Harvard Conference on
Grammatical Relations. Bloomington, Indiana University Linguistics Club.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
Since words (lexical signs) in HPSG are highly
structured, together with the principles mentioned, the
sharing of information is constrained between lexical
signs and phrasal signs which they head (“projections”
or the projection principle of GB theories).
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
HPSG principles are more explicitly formulated and thus
implementations more likely to be faithful to theory. There is less
work for language-specific rules of grammar. In Pollard & Sag
(1987) only four highly schematic HPSG rules accounted for a
substantial English fragment. One rule, informally written as
[ SUBCAT   ]  H[ LEX - ], C
subsumes a number of conventional phrase structure rules, such
as those below.
S  NP VP
NP  DET NOM
NP  NP’s NOM
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
In the HPSG rule, one possibility is that the English phrase to be
a saturated sign [ SUBCAT   ], with   denoting the empty list,
has constituents which are a phrasal head (H[ LEX - ]) and a
single complement (C).
Another HPSG rule, expressed informally as
[ SUBCAT [ ] ]  H[ LEX + ], C*
says that another option for English phrases is to be a sign
subcategorizing for exactly one complement [ SUBCAT [ ] ] with
“[ ]” stands for any list of length one, and whose daughters are a
lexical head (H[ LEX + ]) and any number of complement
daughters.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
This rule subsumes a number of conventional phrase structure
rules, such as
VP  V; VP  V S’; AP  A;
VP  V NP; AP  A PP; PP  P NP;
VP  V PP; VP  V VP; VP  V AP;
VP  V NP NP; VP  V NP PP; etc.
HPSG rules determine constituency only; this follows GPSG
theory where generalizations about relative order of constituents
is factored out of phrase structure rules and expressed in
independent language-specific linear precedence (LP)
constraints. Unlike GPSG’s some LP constraints may refer not
only to syntactic categories but also to their grammatical relations
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
Additional lexicalization of linguistic information and
further simplification of the grammar is achieved in
HPSG by lexical rules (similar to that of LFG). Lexical
rules operate upon lexical signs of a given input class,
systematically affecting their phonology, semantics
and syntax to produce lexical signs of a certain output
class.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
HPSG is not a theory of syntax. Researchers into GB,
GPSG, and LFG have focussed on syntax, relying
mainly on a Montague-style system of model-theoretic
interpretation. In contrast, HPSG theory inextricably
intertwines syntax and semantics, that is, syntactic
and semantic aspects of grammatical theory are built
up in an integrated way from the start. Thus HPSG is
closer in spirit to situation semantics, and this
closeness is reflected in the choice of ontological
categories in terms of which the semantic contents of
signs are analyzed: individuals, relations, roles,
situations and circumstances.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
The semantic content of a simple declarative sentence is a
circumstance, a situation-theoretic object composed of individuals
playing roles in a relation. This formulation is a more precise
account of the earlier conceptual dependency theory and preference
semantics formalisms of the early 1970’s. Thus, the semantic
content of the sentence John admires Jane is as follows:
RELATION
ADMIRER
ADMIREE
ADMIRE
JOHN
JANE
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
The semantic content of sentences, and of phrases in general, is
determined by various pieces of syntactic and semantic information
associated with their constituents, in conjunction with universal
linguistic principles (and contextual factors). In the example above,
John and Jane are part of the semantic contents of the subject NP
John and the direct object NP Jane.
The relation ADMIRE and the assignment of the ADMIRER and
ADMIREE roles to the subject and direct object come from the head
verb admires, which has the following form:
 admires, V[SUBCAT NPi, NPj ,
RELATION
ADMIRER
ADMIREE
ADMIRE
i
j
Instructor: Nick Cercone - 3050 CSEB - [email protected]

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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
The lexical sign consists of phonological, syntactic, and semantic
information. The crucial assignment of semantic roles to grammatical
relations is mediated by the SUBCAT feature. i and j are variables. The
specification “NPi” calls for an NP whose variable is to be unified with the
ADMIREE role filler. The subcategorization principle ensures that
variables j and i are then unified with John and Jane. The semantic
content of the whole sentence follows by an additional universal
Semantic Principle which requires the semantic content of a phrase be
unified with that of its head daughter. Whereas Montague style
semantics are determined by syntax directed model theoretic
interpretation, in HPSG theory the semantic contents of a sentences’
lexical constituents “falls out” by virtue of the linguistic constraints which
require pieces of information associated with signs be unified with other
pieces.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
22
CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG
•
tuple (Atom, Feat, Var, Type, Init, Rule):
• Atom - set of atoms
• Feat - set of features or attributes
• Type = (T, subtype) - type hierarchy
• Init - set of initial AVMs (attribute-value matrices)
• Rule - set of rules
•
HPSG principes are defined and used to define HPSG
modules
Instructor: Nick Cercone - 3050 CSEB - [email protected]
23
CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG mechanism
shift to HPSG illustration slide
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG Principles
• Principles have the same form as HPSG rules:
[]→[][][]…[]
Unlike HPSG rules, principles are not applied directly.
 Instead, principles are unified with HPSG rules:
• P  R = { p Ụ r : p P, r R, and p Ụ r exists } 
•
{ r : r R, for all p P, p Ụ r does not exist }
 P  R is used as the set of rules instead of R

Instructor: Nick Cercone - 3050 CSEB - [email protected]
25
CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG Feature Structure Descriptions
FEATURE1 VALUE1
FEATURE2 VALUE2
...
FEATUREn VALUEn
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
HPSG Feature Structure Descriptions
pizza thing
pizza
topping set
CRUST
TOPPINGS
vegetarian
OLIVES
ONIONS
MUSHROOMS
non-vegetarian
SAUSAGE
PEPPERONI
HAM
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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CSE6390 3.0 Special Topics in AI & Interactive Systems II
Introduction to Computational Linguistics
Fall Semester, 2010
Concluding Remarks
If you know what I mean
A poet should be of the
old-fashioned meaningless brand:
obscure, esoteric, symbolic,
-- the critics demand it;
so if there's a poem of mine
that you do understand
I'll gladly explain what it means
till you don't understand it.
Instructor: Nick Cercone - 3050 CSEB - [email protected]
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