Artificial intelligence

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Transcript Artificial intelligence

Artificial Intelligence
The different levels of language
analysis
Fall 2008
professor: Luigi Ceccaroni
The different levels of language
analysis
• A NL system must use considerable
knowledge about the structure of the
language itself, including:
– What the words are
– How words combine to form sentences
– What the words mean
– How word meanings contribute to sentence
meaning
–…
2
The different levels of language
analysis
• We cannot completely account for linguistic
behavior without also taking into account:
– humans’ general world knowledge
– their reasoning abilities
• For example, to participate in a conversation
it is necessary:
– Knowledge about the structure of the language,
but also
– Knowledge about the world in general
– Knowledge about the conversational setting in
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particular
The different levels of language
analysis
• The following are some of the different
forms of knowledge relevant for NL
understanding:
– Phonetic and phonological knowledge
– Morphological knowledge
– Syntactic knowledge
– Semantic knowledge
– Pragmatic knowledge
– Discourse knowledge
– World knowledge
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Phonetic and phonological
knowledge
• It concerns how words are related to the
sounds that realize them
• Such knowledge is crucial for speechbased systems
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Morphological knowledge
• Use of lexicons
– Reference books containing an alphabetical
list of words with information about them
Lexeme Information
cant-
cantar
V / Infinitive
-o/-es/-a/-em/-eu/-en
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Morphological knowledge
• Versió simple: utilització de formaris (llista
de formes amb informació morfològica i els
lexemes corresponents)
• Morfema = lexema (o arrel) o gramema
Lexema Gramema
cant
o
es
a
em
en
Morphological knowledge
• Analitzadors morfològics:
– Diccionaris de morfemes:
• diccionari d’arrels (lexemes), de sufixes, prefixes, infixes
– Morfotàctica: regles de combinació de morfemes
– Variacions fonològiques: canvis al combinar els
morfemes (ex., ploure, plovisquejar)
• Tipus d’analitzadors
– FSA (finite state automaton)
– FST (finite state transducer)
– cascada de FSTs
Syntactic knowledge
• Detection of tractable units: paragraphs
and sentences:
– Location of marks of punctuation: “.”, “?”, “!”,
“…”
• Problems: acronyms, initials
– Machine learning and classification
techniques
• They take into account contextual information
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Syntactic knowledge
• Detection of units of meaning
– Recognition and adequate grouping of words
• “/Parlarà/ /sens dubte/ /de/ /les/ /reestructuracions/
/urbanes/ /a/ /Sant Cugat/”
• Assignment of grammatical categories
• Addition of semantic information to
lexical units (use of ontologies and
dictionaries)
• Acknowledgment and classification of
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proper names and entities
Syntactic knowledge
• Correspondence between orthographic
and grammatical words
– “dóna-m’ho”, “dímelo” (1 orthographic word, 3
grammatical words)
– “sens dubte”, “sin embargo” (2 orthographic
words, 1 p. grammatical word)
• Homonymy
– Same form, different grammatical categories:
• “wheel” (rueda, ruleta): noun
• “wheel” (empujar): verb
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Syntactic knowledge
• Polysemy
– Same form and category, different meanings:
• “bank” (grupo): data bank, electronic resource bank
• “bank” (banco): bank account, bank balance
• “bank” (ribera): river bank, river + burst its banks
• Acronyms
– “The cell’s DNA sample was identified by
PRC, a process approved by the official UBI.”
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Syntactic knowledge
• Abbreviations
– For example, the word "abbreviation" can itself
be represented by the abbreviation "abbr." or
"abbrev.“
• Formulae and units of measurements
– “One of many famous formulae is Albert
Einstein's E = mc².”
– “In the US the inch is now defined as
0.0254 m, and the avoirdupois pound is now
defined as 453.59237 g.”
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Syntactic knowledge
• Syntactic categories:
•
•
•
•
•
•
•
•
•
•
adjective (ADJ)
adjective phrase (ADJP)
adverb (ADV)
adverbial phrase (ADVP)
article (ART)
auxiliary verb (AUX)
determiner (DET)
noun (N)
noun phrase (NP)
preposition (P)
•
•
•
•
•
•
•
•
prepositional phrase (PP)
pronoun (PRO)
relative clause (REL)
relative pronoun (RELPRO)
quantifying determiner
(QDET)
sentence (S)
verb (V)
verb phrase (VP)
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Syntactic knowledge
– Problema de la granularitat (verb ->
transitiu/intransitiu)
– Propietats sintàctiques de concordança
• gènere (masculí/femení)
• nombre (singular/plural)
• persona (primera, segona...)
• cas (acusatiu,datiu..)
Representation
• Altres propietats sintàctiques:
– Tipus de complement del verb
– Preposicions que accepta una paraula
• Categoria semàntica
• Informació morfològica
– Derivació: prefixos/infixos/sufixos
plov + -isquej- + ar
re- + estructura + -cio + -ns
prefix
arrel
sufix
sufix
Representation
• Informació lèxica
repetició
nom
plural
re- + estructura + -cio + -ns
prefix
arrel
sufix
sufix
Representation
• Informació lèxica
diminutiu
infinitiu
plov + -isquej- + ar
arrel
infix
sufix
Syntax and semantics
• Examples:
– John sold the book to Mary.
– The book was sold to Mary by John.
– *After it fell in the river, John sold the book to Mary.
– After it fell in the river, the book was sold to Mary by John.
– *John are in the corner.
– *John put the book.
– Flying planes are dangerous.
– Flying planes is dangerous.
Collaboration between parsers
Anàlisi Sintàctica
• sense sintaxi
• sense semàntica
• procés en cascada (1)
– sintaxi | semàntica
Interpretació Semàntica
• procés en cascada (2)
– {sintaxi + filtre semàntic} |
semàntica
• procés en paral·lel
– {sintaxi, semàntica}
Pre-process
•
•
•
•
•
•
•
Segmentació
Localització d’unitats (paraules)
Lematització, anàlisi morfològica
Desambiguació morfosintàctica (POS-tagging)
Etiquetat semàntic
Desambiguació semàntica (WSD)
Detecció i classificació d‘entitats amb nom
(named entity recognition, NER)
Quina es la capital de França?
resultat de l'anàlisi morfològica
quina
és
la
capital
de
França
?
quin
ésser
el
capital
de
frança
?
DT0FS00
VMIP3S0
TDFS0
AQPCS00
SPS00
NP00000-loc
Fit
resultat del POS-tagging
quina
és
la
capital
de
França
?
quin
ésser
el
capital
de
frança
?
DT0FS00
VMIP3S0
TDFS0
NCFS000
SPS00
NP00000-loc
Fit
quina
NCFS000
ell
capital
PP3FSO00
NCFS000
Example
la
capital
I
NCMS000
Post-process
• Anàlisi semàntica - pragmàtica
• Anàlisi il·locutiva
– Reconeixement d’intencions
The component steps of
communication
• A typical communication episode, in which
speaker S wants to inform hearer H about
proposition P using words W, is composed of 7
processes:
– Intention. Speakers S decides that there is some
proposition P that is worth saying to hearer H.
– Generation. The speaker plans how to turn the
proposition P into an utterance that makes it likely
that the hearer can infer the meaning P (or something
close to it).
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The component steps of
communication
– Synthesis. The speaker produces the
physical realization W’ of the words W. This
can be via ink on paper, vibrations in air, or
some other medium.
– Perception. H perceives W’ as W2’ and
decodes it as the words W2. When the
medium is speech, the perception is called
speech recognition; when it is printing, it is
called optical character recognition (OCR).
Both are now commonplace.
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The component steps of
communication
– Analysis. We divide it into 3 main parts:
• Syntactic interpretation (or parsing) is the process of
building a parse tree for an input string. The interior nodes
of the parse tree represent phrases and the leaf nodes
represent words.
• Semantic interpretation is the process of extracting the
meaning of an utterance. Utterances with several possible
interpretations are said to be ambiguous.
• Pragmatic interpretation takes into account the fact that the
same words can have different meanings in different
situations.
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The component steps of
communication
– Disambiguation. H infers that S intended to convey
Pi (where ideally Pi = P). Communication works
because H does the work of figuring out which
interpretation is the one S probably meant to convey.
Disambiguation is a process that depends heavily on
uncertain reasoning.
– Incorporation. H decides to believe Pi (or not). A
totally naive agent might believe everything it hears.
A sophisticated agent treats the speech act as
evidence for Pi, not confirmation of it.
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Syntactic analysis
• Objectives:
– Determining if a sentence is syntactically
correct
– Creating a structure with information which
can be used during the semantic analysis
Syntactic analysis
• Alphabet (vocabulary): Σ
• Concatenation operations
• Σ* (free monoid): set of all strings that can
be formed with symbols of Σ
• Language: L ⊆ Σ*
• Given a string w1n of Σ*:
w1n = w1, …, wn
wi ∈ Σ
– We have to determine if w1n ∈ L
Ways to define membership
• Grammar
– G ⇒ L(G)
– w1n ∈ L(G) ?
• Language model
– P(w1n)
– si P(w1n) > 0 ⇒ w1n ∈ L
• Corpora (sentences, patterns), which
define correct sentences:
• Syntactic dictionaries
• Composition rules
Most usual way: grammar
<V, Σ, P, S>
Non-terminal vocabulary
(set of variables)
Initial variable
Production set
Terminal vocabulary
(alphabet)
Σ ∩ V=Ø
Σ ∪ V = vocabulary
S∈V
Grammars and parsing
• To examine how the syntactic structure of a
sentence can be computed:
– Grammar, a formal specification of the structures
allowable in the language
– Parsing technique, the method of analyzing a
sentence to determine its structure according to the
grammar
• The most common way of representing how a
sentence is broken into its major subparts
(constituents), and how those subparts are
broken up in turn, is a tree.
Grammars and sentence
structure
• Tree representation for the sentence Adrià
menja el bacallà:
S
VP
NP
NAME
NP
V
ART
Adrià
menja
el
N
bacallà
Grammars and sentence
structure
• The sentence (S) consists of an initial noun phrase (NP)
and a verb phrase (VP).
• The initial noun phrase is made of the simple NAME
Adrià.
• The verb phrase is composed of a verb (V) menja and
an NP, which consists of an article (ART) el and a
common noun (N) bacallà.
• In list notation this same structure could be represented
as:
(S
(NP (NAME Adrià))
(VP (V menja)
(NP (ART el)
(N bacallà) )))
Grammars and sentence
structure
•
•
•
•
To construct a tree structure for a sentence, you must
know what structures are legal.
A set of rewrite rules describes what tree structures
are allowable.
These rules say that a certain symbol may be
expanded in the tree by a sequence of other symbols.
A set of rules constitutes a grammar:
1.
2.
3.
4.
5.
6.
7.
8.
S → NP VP
VP → V NP
NP → NAME
NP → ART N
NAME → Adrià
V → menja
ART → el
N → bacallà
Grammars and sentence
structure
• Rule 1 says that an S may consist of an NP followed by
a VP.
• Rule 2 says that a VP may consist of a V followed by an
NP.
• Rules 3 and 4 say that an NP may consist of a NAME or
may consist of an ART followed by an N.
• Rules 5 - 8 define possible words for the categories.
• Grammars consisting entirely of rules with a single
symbol on the left-hand side, called the mother, are
called context-free grammars (CFGs).
Grammars and sentence
structure
• Context-free grammars (CFGs) are a very important class of
grammars because:
– the formalism is powerful enough to describe most of the structure in
natural languages,
– yet is restricted enough so that efficient parsers can be built to
analyze sentences.
• Symbols that cannot be further decomposed in a grammar (the
words Adrià, menja…) are called terminal symbols.
• The other symbols, such as NP and VP, are called nonterminal
symbols.
• The grammatical symbols such as N and V that describe word
categories are called lexical symbols.
• Many words will be listed under multiple categories. For example,
poder would be listed under V (can) and N (power).
• Grammars have a special symbol called the start symbol. Usually,
the start symbol is S (also meaning sentence).
Grammars and sentence
structure
• A grammar is said to derive a sentence if there is a
sequence of rules that allow you to rewrite the start
symbol into the sentence, for instance, Adrià menja el
bacallà.
• This can be seen by showing the sequence of rewrites starting from
the S symbol, as follows:
S
=> NP VP
=> NAME VP
=> Adrià VP
=> Adrià V NP
=> Adrià menja NP
=> Adrià menja ART N
=> Adrià menja el N
=> Adrià menja el bacallà
(rewriting S)
(rewriting NP)
(rewriting NAME)
(rewriting VP)
(rewriting V)
(rewriting NP)
(rewriting ART)
(rewriting N)
Grammars and sentence
structure
• Two important processes are based on
derivations:
– The first is sentence generation, which uses
derivations to construct legal sentences. A simple
generator could be implemented by randomly
choosing rewrite rules, starting from the S symbol,
until you have a sequence of words. The preceding
example shows that the sentence Adrià menja el
bacallà can be generated from the grammar.
– The second process based on derivations is parsing,
which identifies the structure of sentences given a
grammar.
Parsing as a search procedure
• In derivations, there are two basic
methods of searching:
– A top-down strategy starts with the S symbol and
then searches through different ways to rewrite the
symbols until the input sentence is generated, or until
all possibilities have been explored. The preceding
example demonstrates that Adrià menja el bacallà is
a legal sentence by showing the derivation that could
be found by this process.
Parsing as a search procedure
• In a bottom-up strategy, you start with the words in the
sentence and use the rewrite rules backward to reduce
the sequence of symbols until it consists solely of S. The
left-hand side of each rule is used to rewrite the symbol
on the right-hand side. A possible bottom-up parse of
the sentence Adrià menja el bacallà is:
=> NAME menja el bacallà (rewriting Adrià)
=> NAME V el bacallà (rewriting menja)
=> NAME V ART bacallà (rewriting el)
=> NAME V ART N (rewriting bacallà)
=> NP V ART N (rewriting NAME)
=> NP V NP (rewriting ART N)
=> NP VP (rewriting V NP)
=> S (rewriting NP VP)
• A tree representation can be viewed as a record of the
CFG rules that account for the structure of the sentence.
What makes a good grammar
• In constructing a grammar for a language,
you are interested in:
– generality, the range of sentences the
grammar analyzes correctly;
– selectivity, the range of non-sentences it
identifies as problematic;
– understandability, the simplicity of the
grammar itself.
Generative capacity
• Grammatical formalisms based on rewrite rules
can be compared according to their generative
capacity, which is the range of languages that
each formalism can describe.
• It turns out that no natural language can be
characterized precisely enough to define the
generative capacity.
• Formal languages, however, allow a precise
mathematical characterization.
Generative capacity
• Consider a formal language consisting of the symbols a,
b, c and d (think of these as words).
• Then consider a language L1 that allows sequences of
letters in alphabetical order. For example, abd, ad, bcd
and abcd are all legal sentences. To describe this
language, we can write a grammar in which the righthand side of every rule consists of one terminal symbol
possibly followed by one nonterminal.
• Such a grammar is called a regular grammar. For L1
the grammar would be:
S -> a S1
S -> b S2
S -> c S3
S -> d
S1 -> b S2
S1 -> c S3
S1 -> d
S2 -> c S3
S2 -> d
S3 -> d
Generative capacity
• Consider another language, L2, that
consists only of sentences that have a
sequence of a’s followed by an equal
number of b’s—that is, ab, aabb, aaabbb,
and so on. You cannot write a regular
grammar that can generate L2 exactly.
• A context-free grammar to generate L2,
however, is simple:
S -> a b
S -> a S b
Generative capacity
•
•
•
•
Some languages cannot be generated by a CFG.
One example is the language that consists of a sequence of a’s,
followed by the same number of b’s, followed by the same number
of c's - that is, abc, aabbcc, aaabbbccc, and so on.
Similarly, no context-free grammar can generate the language that
consists of any sequence of letters repeated in the same order
twice, such as abab, abcabc, acdabacdab, and so on.
There are more general grammatical systems that can generate
such sequences, however. One important class is the contextsensitive grammar, which consists of rules of the form:
αAβ→αψβ
where A is a symbol, α and β are (possibly empty) sequences of
symbols, and ψ is a nonempty sequence of symbols.
Generative capacity
• Even more general are the type 0 grammars,
which allow arbitrary rewrite rules.
• Work in formal language theory began with
Chomsky (1956). Since the languages
generated by regular grammars are a subset of
those generated by context-free grammars,
which in turn are a subset of those generated by
context-sensitive grammars, which in turn are a
subset of those generated by type 0 languages,
they form a hierarchy of languages (called the
Chomsky Hierarchy).
Languages associated to
Chomsky-hierarchy grammars
Grammar
Languages
Automaton
Type-0
Recursively
enumerable
Turing machine
Type-1
Linear-bounded
Context-sensitive non-deterministic
Turing machine
Type-2
Context-free
Non-deterministic
pushdown
automaton
Regular
Finite state
automaton
Type-3
Grammaticality condition
A sentence w (a string of Σ*) pertains to
the language generated by grammar G, if
grammar G can derive w starting from S,
using production rules.
Obtaining the grammar
• Definition of the terminal tagset (Σ)
• Definition of the non-terminal tagset (V)
• Definition of grammar rules (P):
– Manual construction
– Automatic construction
• Grammatical inference (induction)
– Semiautomatic construction
Grammars for language
processing
•
•
•
•
Minimum: context-free grammars (CFGs)
Is NL a context-free language? No.
Are CFGs sufficient? No.
Solutions:
– CFG + {procedural addition of context}
– Logical grammars (unification)
– Grammars enriched with statistical information
(SCFGs)
–…
CFG parsers and extensions
• Let’s start from a simplification of CFGs
• CFGs ⇒ RGs
• Finite state automata (FSAs)
• Extension of FSAs
• TNs (Transition Networks) ⇒ RTNs (Recursive
Transition Networks) ⇒ ATNs (Augmented Transition
Networks)
• W. A. Woods (1970) in "Transition Network Grammars for
Natural Language Analysis" claims that by adding a recursive
mechanism to a finite state model, parsing can be achieved
much more efficiently.
• Charts (M. Kay, 1980)
• WFSTs (well-formed substring tables)
• …
Transition networks (TNs)
• Autòmat finit
– Estats associats a parts de la frase
– Transicions
• Etiquetes que fan referència a categories
morfosintàctiques
– Una transició és acceptable si la paraula té la mateixa
categoria que apareix etiquetada a l’arc
– No determinisme
• Més d’un estat inicial
• Una paraula amb més d’una categoria possible
• Més d’un arc per la mateixa categoria
TNs: example
DET
ADJ
q1
q0
DET
N
q2
V
q4
q5
N
V
NAME
q3
El gat menja bacallà
DET N
V
N
N
q6
ADJ
TNs: limitations
• Limitat a llenguatges regulars
• No es pot dir que analitzi
– Reconeix
• No-determinisme ⇒ backtracking
– Ineficiència
• No separació entre gramàtica i
analitzador
– gramàtica ⇒ descripció del model sintàctic
– analitzador (parser) ⇒ control
Recurrent TNs (RTNs)
• Col·lecció de xarxes de transició (TNs)
etiquetades amb un nom
– Arcs
• Etiquetats amb categories → com xarxes normals
– Etiquetes terminals
• Etiquetats amb identificadors de xarxes de
transició (TNs)
– Etiquetes no terminals: els estats finals de les TNs
causen el retorn a l’estat destí de la transició que ha
causat la crida
• Les RTN son dèbilment equivalents a les
CFG
RTNs: examples
NP
S
2
VP
3
1
NP
N
DET
1
2
PP
3
N
ADJ
NAME
RTNs: examples
V
1
VP
NP
2
3
V
P
PP
1
NP
2
3
RTNs: limitations
• Transicions només depenen de les
categories (poc expressiu)
– Llenguatge de context lliure
• Reconeixen però no analitzen
• Ineficiència inherent al backtracking
Charts
• Intenten eliminar redundàncies en l’anàlisi
(alleugeriment del cost del backtracking)
memoritzant estructures parcials ja
construïdes.
• No afecten l’estratègia de l’anàlisi
• Inconvenients: espai, temps de construcció,
només guarden components ben formats
Charts
• Chart = graf dirigit que es construeix de manera
dinàmica i incremental a mesura que es realitza
l’anàlisi.
• Els nodes corresponen al principi i final de la
frase i a les separacions entre paraules (N+1
nodes)
1
La
2
frase
3
a
4
analitzar
5
és
6
aquesta
7
Charts
• Els arcs es creen dinàmicament. Un arc de la
posició i a la j (j ≥ i) engloba totes les paraules que
estan entre la posició i i la j.
• Els arcs poden ser
• actius = objectius o hipòtesis per completar
• inactius = components completament analitzades
La
1
frase
2
a
3
analitzar
4
és
5
aquesta
6
7
Charts: notation
• Regla puntejada (DR, “dotted rule”):
producció de la gramàtica que conté
algun punt en la seva part dreta.
Per exemple, de la regla A −> BCD es poden
derivar les següents regles puntejades:
A −> . B C D
A −> B . C D
A −> B C . D
A −> B C D .
(corresponent a un arc actiu)
”
”
(corresponent a un arc inactiu)
Charts: notation
Arc d’un chart: < i , j , X → a.b >
i,j:
X → ab
X → a.b
nodes origen i destí
producció de la gramàtica
DR
< 3, 3 , VP → .V NP >
< 1, 3 , S → NP.VP >
< 3, 5 , VP → V NP.>
1
El
2
gat
3
menja
4
salmó
5
Basic rule of combination
Arc actiu: <i, j, A → a.Bb>
Arc inactiu:
<j, k, B → g.>
Resultat: <i, k, A → aB.b>
Ascendant strategy
• Regla bàsica: Cada vegada que s’afegeix
un arc inactiu al Chart <i, j, A → a.>,
aleshores s’ha d’afegir al seu extrem
esquerre un arc actiu <i, i, B → .Ab > per
cada regla B → Ab de la gramàtica
• Inicialització: afegir els arcs inactius que
corresponen a les categories lèxiques
(terminals). Ex: <1, 2, Det → el.>
Descendant strategy
Regla bàsica: Cada vegada que s’afegeix un arc actiu al
Chart < i, j, A → a.Bb >, aleshores, per cada regla B → b de
la gramàtica, s’ha d’afegir un arc actiu al seu extrem dret < j,
j, B →.b >
Inicialització: Igual que abans però a més cal afegir l’arc
actiu que correspon a l’objectiu d’obtenir una frase.
Ex: <1, 1, oració → .SN SV>
La regla bàsica de combinació amb l’estratègia
ascendent o descendent (o una combinació de les
dues) és el que ens proporciona el mètode d’anàlisi
Charts: example
[Oracio → GN GV •]
[Oracio → GN GV •]
[Oracio → GN • GV]
[GN → n •]
[GV → • vi]
[Oracio → • GN GV]
[GV → • vt GN]
[GN → det • n]
[GN → • det n]
[GN → • n]
[GN → • det n]
[GN → det n •]
[det]
el
0
1
[GV → vt • GN]
[GV → vi •][GN → • n]
[n]
[vt] [vi]
[n]
gat
menja
peix
2
3
4
Features (rasgos)
• Context-free grammars provide the basis for
most of the computational parsing mechanisms
developed to date.
• As they have been described, they would be
inconvenient for capturing natural language.
• The basic context-free mechanism can be
extended defining constituents by a set of
features.
• This extension allows aspects of natural
language such as agreement and
subcategorization to be handled in an intuitive
and concise way.
Feature systems and
augmented grammars
• In natural language there are often
agreement restrictions between words and
between phrases.
• For example, the noun phrase (NP) un
hombres is not correct because the article
un indicates a single object while the noun
hombres indicates a plural object.
• The NP does not satisfy the number
agreement restriction.
Feature systems and
augmented grammars
• There are many other forms of agreement, including
– subject-verb agreement
– gender agreement for pronouns
– restrictions between the head of the phrase and the form of its
complement.
• Features are introduced to handle such phenomena.
• A feature NUMBER might be defined that takes a value
of either s (for singular) or p (for plural) and we then
might write an augmented CFG rule such as
NP → ART N only when NUMBER1 agrees with NUMBER2
• This rule says that a legal NP consists of an article
(ART) followed by a noun (N), but only when the number
feature of the first word agrees with the number feature
of the second.
Feature systems and
augmented grammars
NP → ART N only when NUMBER1 agrees with NUMBER2
• This one rule is equivalent to two CFG rules that would
use different terminal symbols for encoding singular and
plural forms of all NPs, such as
NP-SING → ART-SING N-SING
NP-PLURAL → ART-PLURAL N-PLURAL
• The two approaches seem similar in ease-of-use in this
one example.
• Though, in the second case, all rules in the grammar
that use an NP on the right-hand side would need to be
duplicated to include a rule for NP-SING and a rule for
NP-PLURAL, effectively doubling the size of the
grammar.
Feature systems and
augmented grammars
• Handling additional features, such as person
agreement, would double the size of the
grammar again, and so on.
• Using features, the size of the augmented
grammar remains the same as the original one,
yet accounts for agreement constraints.
• A constituent is defined as a feature structure
(FS), a mapping from features to values that
defines the relevant properties of the
constituent.
Feature systems and
augmented grammars
• Example: a FS for a constituent ART1 that
represents a particular use of the word un:
ART1:
(CAT ART
ROOT un
NUMBER s)
• It is a constituent in the category ART that has
its root in the word un and is singular.
• Usually an abbreviation is used that gives the
CAT value more prominence:
ART1: (ART ROOT un NUMBER s)
Feature systems and
augmented grammars
• FSs can be used to represent larger constituents as
well.
• FSs themselves can occur as values.
• Special features based on the integers (1, 2, 3…) stand
for the subconstituents (first, second…).
• The representation of the NP constituent for the phrase
un pez could be:
NP1: (NP
NUMBER s
1 (ART
ROOT un
NUMBER s)
2 (N ROOT pez
NUMBER s))
Feature systems and
augmented grammars
• The previous one can also be viewed as a
representation of a parse tree:
• Subconstituent features 1 and 2 correspond to
the subconstituent links in the tree.
Feature systems and
augmented grammars
• The rules in an augmented grammar are stated
in terms of FSs rather than simple categories.
• Variables are allowed as feature values so that
a rule can apply to a wide range of situations.
• For example, a rule for simple NPs would be as
follows:
(NP NUMBER ?n): (ART NUMBER ?n) (N NUMBER ?n)
• This says that an NP constituent can consist of
two subconstituents, the first being an ART and
the second being an N, in which the NUMBER
feature in all three constituents is identical.
Feature systems and
augmented grammars
(NP NUMBER ?n): (ART NUMBER ?n) (N NUMBER ?n)
• According to this rule, constituent NP1 given previously is a legal
constituent.
• The constituent
*(NP 1 (ART NUMBER s)
2 (N NUMBER s))
is not allowed by this rule because there is no NUMBER feature in
the NP.
• The constituent
*(NP NUMBER s
1 (ART NUMBER s)
2 (N NUMBER p))
is not allowed because the NUMBER feature of the N constituent is
not identical to the other two NUMBER features.
Feature systems and
augmented grammars
• Variables are also useful in specifying ambiguity in a
constituent.
• The word crisis is ambiguous between a singular and a
plural reading.
• The word might have two entries in the lexicon that differ
only by the value of the NUMBER feature.
• Alternatively, we could define a single entry that uses a
variable as the value of the NUMBER feature:
(N ROOT crisis NUMBER ?n)
• This works because any value of the NUMBER feature
is allowed for the word crisis.
Feature systems and
augmented grammars
• In many cases not just any value would work, but a
range of values is possible.
• We introduce constrained variables, which are
variables that can only take a value out of a specified
list.
• For example, the variable ?n{s p} would be a variable
that can take the value s or the value p.
• When we write such variables, we will drop the variable
name altogether and just list the possible values.
• The word crisis might be represented by the constituent:
(N ROOT crisis NUMBER ?n{s p})
or more simply as
(N ROOT crisis NUMBER {s p})
Feature systems and
augmented grammars
• There is an interesting issue of whether an augmented
CFG can describe languages that cannot be described
by a simple CFG.
• The answer depends on the constraints on what can be
a feature value.
• If the set of feature values is finite, then it would always
be possible to create new constituent categories for
every combination of features. Thus it is expressively
equivalent to a CFG.
• If the set of feature values is unconstrained then such
grammars have arbitrary computational power.
• In practice, even when the set of values is not explicitly
restricted, this power is not used, and the standard
parsing algorithms can be used on grammars that
include features.
ATN: example
TRETS: Number: Singular, Plural
Person: 1st, 2nd, 3rd
6:Proper
Default: empty
Default: 3rd
ROL: Nucli-Subjecte
5:Pronoun
1:det
f
g
4:Noun
8: Send
h
7:pp
2: Jump
3: Adjective
Xarxa per a reconèixer grups nominals (NP)
ATN: example
Inicialitzacions, condicions i accions
NP-1: fDeterminerg
A: Set Number to the number of *
NP-4: gNounh
C: Number is empty or number is the number of *
A: Set Number to the number of *
Set Nucli-Subjecte to *
NP-5: fPronounh
A: Set Number to the number of *
Set Person to the Person of *
Set Nucli-Subjecte to *
NP-6: fProperh
A: Set Number to the number of *
Set Nucli-Subjecte to *
ATN: limitations
• Són adequades per l’anàlisi descendent, però no
resulta fàcil implementar una anàlisi ascendent o
híbrida.
• Redundància de les operacions de backtracking:
– ineficiència
• Problemes d’expressivitat notacional:
– la gramàtica es barreja amb les accions
CFG recognition using
difference lists
• An efficient implementation of CFGs can
be obtained by making use of difference
lists: a sophisticated Prolog technique.
• The key idea underlying difference lists is
to represent the information about
grammatical categories not as a single list,
but as the difference between two lists.
• For example, instead of representing a
woman shoots a man as
[a,woman,shoots,a,man] we might
represent it as the pair of lists
[a,woman,shoots,a,man] [ ].
CFG recognition using
difference lists
• Think of the first list as what needs to be
consumed (or if you prefer: the input list), and
the second list as what we should leave
behind (or: the output list).
• Viewed from this (rather procedural)
perspective the difference list
[a,woman,shoots,a,man] [ ].
• represents the sentence a woman shoots a
man because it says: If I consume all the
symbols on the left, and leave behind the
symbols on the right, I have the sentence I
am interested in.
CFG recognition using
difference lists
• The sentence we are interested in is the difference
between the contents of the two lists.
• Difference representations are not unique.
• In fact, we could represent a woman shoots a man in
infinitely many ways.
• For example, we could also represent it as
[a,woman,shoots,a,man,ploggle,woggle] [ploggle,woggle].
• Again the point is: if we consume all the symbols on the
left, and leave behind the symbols on the right, we have
the sentence we are interested in.
CFG recognition using
difference lists
• If we bear the idea of consuming something, and leaving something
behind in mind, we obtain the following recognizer (Prolog notation):
s(X,Z) :- np(X,Y), vp(Y,Z).
np(X,Z) :- det(X,Y), n(Y,Z).
vp(X,Z) :- v(X,Y), np(Y,Z).
vp(X,Z) :- v(X,Z).
det([the|W],W).
det([a|W],W).
n([woman|W],W).
n([man|W],W).
v([shoots|W],W).
The s rule says: I know that the pair of lists X and Z represents a
sentence if (1) I can consume X and leave behind a Y, and the
pair X and Y represents a noun phrase, and (2) I can then go on to
consume Y leaving Z behind, and the pair Y Z represents a verb
phrase.
CFG recognition using
difference lists
• The idea underlying the way we handle
the words is similar.
• The code
n([man|W],W).
• means we are handling man as the
difference between [man|W] and W.
• Intuitively, the difference between what I
consume and what I leave behind is
precisely the word man.
CFG recognition using
difference lists
• How do we use such grammars? Here's
how to recognize sentences:
s([a,woman,shoots,a,man],[]).
yes
• This asks whether we can get an s by
consuming the symbols in
[a,woman,shoots,a,man], leaving nothing
behind.
CFG recognition using
difference lists
• Similarly, to generate all the sentences in the grammar,
we ask
s(X,[]).
• This asks: what values can you give to X, such that we
get an s by consuming the symbols in X, leaving nothing
behind?
• The queries for other grammatical categories also work
the same way.
• For example, to find out if a woman is a noun phrase we
ask:
np([a,woman],[]).
CFG recognition using
difference lists
• And we generate all the noun phrases in
the grammar as follows:
np(X,[]).
• It has to be admitted that this recognizer is
not as easy to understand, at least at first,
and it's a pain having to keep track of all
those difference list variables.
• This is where DCGs come in.