Download a woman shoots a man

Inteligencia Artificial
Interpretación semántica
Primavera 2009
profesor: Luigi Ceccaroni
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.
Formalismos de unificación
• La unificación se usa como mecanismo básico
de composición entre constituyentes en
gramáticas lógicas.
• Història:
– Q-Systems (Colmerauer, 1972)
– Prolog (Colmerauer, 1973)
– Gramàtiques de Metamorfosi (Colmerauer,
1975)
– Gramàtiques de Clàusules Definides (DCGs)
(Pereira, Warren, 1980)
Análisis gramatical con
unificación
• Gramática
(1) oració (X,Y)
(2) gnom(X,Y)
(3) gver(X,Y)
• Lexicón
(4) art(X,Y)
(5) nom(X,Y)
(6) ver(X,Y)
:- gnom(X,Z), gver(Z,Y)
:- art(X,Z), nom(Z,Y)
:- ver(X,Y)
:- el(X,Y)
:- gos(X,Y)
:- borda(X,Y)
Análisis gramatical con
unificación
1
el
2
gos
3
borda
(7) el(1,2)
(8) gos(2,3)
(9) borda(3,4)
Frase a analizar: oració(1,4)
4
Análisis gramatical con
unificación
1
el
2
gos
3
borda
4
oració(1,4)
(R1) (X  1, Y 4) por unificación
gnom (1,Z), gver(Z,4)
(R2) aplicada a gnom(1,Z)
art(1,U), nom(U,Z), gver(Z,4)
Análisis gramatical con
unificación
1
el
2
gos
3
borda
4
art(1,U), nom(U,Z), gver(Z,4)
(R4) aplicada a art(1,U)
el(1,U), nom(U,Z), gver(Z,4)
(R7) (U  2)
el(1,2), nom(2,Z), gver(Z,4)
nom(2,Z), gver(Z,4)
Análisis gramatical con
unificación
1
el
2
gos
nom(2,Z), gver(Z,4)
(R5)
gos(2,Z), gver(Z,4)
(R8) (Z  3)
gos(2,3), gver(3,4)
gver(3,4)
3
borda
4
Análisis gramatical con
unificación
1
gver(3,4)
(R3)
ver(3,4)
(R6)
borda(3,4)
(R9): Fin
el
2
gos
3
borda
4
Análisis semántico
• Consiste en construir una representación de las
frases en algún sistema formal.
• En general es un problema intratable.
• Se simplifica suponiendo que la semántica de una
frase se pueda construir a partir de la semántica de
sus partes: semántica compositiva.
• Algunas características del lenguaje se tienen que
tratar a parte: referencias, omisiones, contexto…
Estrategias de análisis
• Dos maneras de plantear la
interpretación semántica:
– Secuencial (sintáctica → semántica)
– Paralela (sintáctica + semántica)
Interpretación secuencial
• Problemas de ambigüedad
– Es posible que haya más de una
interpretación sintáctica.
– Hay que considerarlas todas, para poder
comprobar sucesivamente cuáles son las
semánticamente posibles.
• Principal ventaja
– El análisis semántico parte de un análisis
sintáctico correcto.
Interpretación paralela
• Principal problema
– No se sabe si la interpretación sintáctica es
correcta hasta el final.
• Principal ventaja
– Poder descartar interpretaciones sintácticas
correctas (o parcialmente correctas) que no
tengan interpretación semántica asociada.
• Las reglas sintácticas incluyen la
información semántica asociada.
– Se obtiene como resultado un árbol de
análisis y una o varias interpretaciones.
Sistema de representación
• El sistema de representación tiene que
permitir:
– Manejar cuantificación, predicación,
negación, modalidad (creencias)
– Resolver la ambigüedad tanto léxica
(polisemia) como sintáctica
– Manejar inferencias (herencia, razonamiento
por omisión)
• Importante a la hora de resolver problemas
que involucren el contexto o el
conocimiento del dominio.
Sistema de representación
• Los sistemas que no se basan en la
sintaxis para la interpretación suelen
utilizar sistemas tipo ontologías.
• Por lo general, se utiliza una variedad de
la lógica de primer orden adecuada al
dominio de aplicación.
• El elemento básico de representación es
el lexema: raíz de un grupo de palabras
que son diferentes formas de “la misma
palabra” (ej.: ir, ido, yendo).
Sistema de representación
• Ejemplos
– Los nombres propios corresponden a constantes.
– Los verbos intransitivos a predicados unarios:
Juan ríe
ríe(juan)
– Los verbos transitivos a predicados de aridad
superior:
Juan lee el Quijote
lee(juan, quijote)
– Los nombres genéricos a predicados sobre
variables:
El hombre hombre(X)
– Los adjetivos a predicados unarios:
La casa grande
grande(X) ∧ casa(X)
Sistema de representación
La representación consiste normalmente en un árbol
de análisis y una función de composición que
construye la interpretación de los elementos
asociados.
S
semS = fS (semNP , semVP)
VP
NP
semNP = fNP (semART , semN)
semART = fART (sem el)
NAME
Adrià
NP
V
menja
ART
N
el
bacallà
La representación del
significado: ejemplo
entrada:
Qui dirigeix el PSOE?
forma lògica:
(pregunta
(referent (X))
(X instancia (X, persona)
(el1 (Y instancia(Y, partit_polític)
nom(Y, "PSOE"))
(Z instancia(Z, dirigir)
present(Z)
valor_prop(Z, agent, X)
valor_prop(Z, pacient,Y)))))
La representación del
significado
• En la anterior forma lógica aparecen 4
tipos diferentes de información:
– Estructura lógica
– Contenido conceptual (semántico)
– Indicación de los actos del discurso
– Anotaciones pragmáticas
• El formalismo de representación debería
proporcionar una capacidad expresiva
suficiente para garantizar la descripción
de estos 4 tipos de información.
Posibles representaciones del
significado
• Lógica de predicados de primer orden
• Otros formalismos lógicos
• Ontologías
27
Representaciones basadas en
lógica
• Un vocabulario de predicados de los que
hay que indicar la aridad (el número de
argumentos y su tipo)
• Un vocabulario de constantes y variables.
• Un conjunto de conectores lógicos.
• Un vocabulario de funciones de las que hay
que indicar la aridad
• Un conjunto de cuantificadores que actúan
sobre los predicados que pueden ser
28
cuantificados.
Semántica y forma lógica
• Semantics = theories of meaning
• Introduction of a level of contextindependent meaning called the logical
form.
– It can be produced directly from the syntactic
structure of a sentence.
– It does not contain the results of any analysis
that requires interpretation of the sentence in
context.
29
Semántica y forma lógica
• Precisely defining the notions of
semantics and meaning is surprisingly
difficult.
– The terms are used for several different
purposes in natural and technical usage.
– There is a use of the verb mean that has
nothing to do with language:
This fire means someone camped here last
night.
30
Semántica y forma lógica
This fire means someone camped here last
night.
• In this example, the fire is evidence for (or
implies) the conclusion.
• The meaning we are interested in is not
this one.
• It is closer to the usage when defining a
word.
31
Semántica y forma lógica
“Amble” means to walk slowly.
• This defines the meaning of a word in
terms of other words.
• We are interested in specifying meaning
without having to refer back to natural
language itself.
• But even if we can do this, defining a
notion of sentence meaning is difficult.
32
Semántica y forma lógica
A guard at the airport: “Do you know what gate
you are going to?”
• If we interpret this as asking whether we
know where we are going, we answer yes.
• But the response can be based on a
misunderstanding, if the guard then asks:
“Which gate is it?”
33
Semántica y forma lógica
“Do you know what gate you are going to?”
• This sentence then appears to mean
different things in different contexts.
• Can we define a notion of sentence
meaning that is independent of context?
• Is there a level at which this sentence has
a single meaning, but may be used for
different purposes?
34
Semántica y forma lógica
• Separating sentence meaning from
sentence usage is complex, but there are
many advantages, primarily modularity.
• If sentences have no context-independent
meaning, then we may not be able to
separate:
– the study of language
– the study of general human reasoning and
context
35
Semántica y forma lógica
• We use the term meaning in a contextindependent sense.
• We use the term usage for the contextdependent aspects.
• The representation of context-independent
meaning is called the logical form.
36
Semántica y forma lógica
• The process of mapping a sentence to its
logical form is called semantic
interpretation.
• The process of mapping the logical form to
the final knowledge representation
language is called contextual
interpretation.
37
Semántica y forma lógica
S
Syntactic analysis
VP
NP
ART
N
la
pelota
V
es
ADJP
roja
semantic interpretation
Logical form
(ROJA1 <LA b1 PELOTA>)
contextual interpretation
Final representation
Roja(BO73)
38
Interpretación semántica:
función de composición
• Interpretación a
través de
evaluaciones lambda:
(lambda (x) (. . .)) =
= ((x) (. . .))
• Gramática:
Oracio  GN FV (2 1)
GN  np (1)
FV  vi (1)
Fv  vt GN (1 2)
• Lexicón:
Pere  np, pere
Maria  np, maria
riu  vi, ((x) (riu(x))
estima  vt , (((x)
((y), estima(y, x))))
39
Función de composición:
ejemplo
40
Función de composición:
ejemplo
41
Gramáticas de cláusulas
definidas (DCGs)
• Las DCGs permiten escribir gramáticas en
forma de programas como, por ejemplo, Prolog.
• Prolog es un lenguaje de reglas que usa
razonamiento hacia atrás como método de
resolución.
• Se define una sintaxis especial que permite
diferenciar los elementos gramaticales de los
procedimientos que se usan para tener en
cuenta el contexto.
42
Gramáticas de cláusulas
definidas (DCGs): sintaxis
• Las reglas usan variables para pasarse
información, hacer las comprobaciones
que exige la gramática o construir un
resultado.
• Se puede introducir código Prolog, entre
llaves:
aaa(W) --> [W], bbb(W), {number(W)}
43
Gramáticas de cláusulas
definidas (DCGs): sintaxis
• Para ejecutar una DCG se llama al
símbolo principal de la gramática con dos
parámetros: una lista con las palabras de
la frase y una lista vacía:
frase([el,gat,menja,bacalla],[])
44
Gramáticas de cláusulas
definidas (DCGs): ejemplo
analisis(X,Y):- asercion(X,Y).
asercion --> sn, verb,compl.
compl --> [].
compl --> prep,sn.
compl--> sn.
sn--> npr.
sn--> det,n.
verb--> [W],{verbo(W)}.
npr--> [W],{npropio(W)}.
n--> [W],{nombre(W)}.
det--> [W],{determ(W)}.
prep--> [W],{prepo(W)}.
npropio(clara).
npropio(maria).
npropio(barcelona).
nombre(hombre).
nombre(profesor).
nombre(libro).
determ(un).
determ(el).
verbo(esta).
verbo(rie).
verbo(piensa).
verbo(habla).
verbo(lee).
prepo(en).
prepo(con).
prepo(de).
45
What are definite clause
grammars?
• Definite Clause Grammars (DCGs) are
convenient ways to represent grammatical
relationships for various parsing
applications.
• They can be used for natural language
work, for creating formal command and
programming languages.
• Quite simply, they are a nice notation for
writing grammars that hides the underlying
difference list variables.
DCGs
• A little grammar written as a DCG:
s --> np, vp.
np --> det, n.
vp --> v, np.
vp --> v.
det --> [the].
det --> [a].
n --> [woman].
n --> [man].
v --> [shoots].
• How do we use this DCG? In fact, we use it in
exactly the same way as we used the difference
list recognizer.
DCGs
• For example, to find out whether a woman
shoots a man is a sentence, we pose the
query:
s([a,woman,shoots,a,man],[]).
• That is, just as in the difference list
recognizer, we ask whether we can get an
s by consuming the symbols in
[a,woman,shoots,a,man], leaving nothing
behind.
DCGs
• Similarly, to generate all the sentences in the
grammar, we pose the query:
s(X,[]).
• This asks what values we can give to X, such
that we get an s by consuming the symbols in
X, leaving nothing behind.
• Moreover, the queries for other grammatical
categories also work the same way. For
example, to find out if a woman is a noun
phrase we pose the query:
np([a,woman],[]).
DCGs
• We generate all the noun phrases in the
grammar as follows:
np(X,[]).
• Quite simply, this DCG is a difference list
recognizer!
• That is, DCG notation is essentially
syntactic sugar: user friendly notation
that lets us write grammars in a natural
way.
DCGs
• The Prolog language can translate this
notation into the kinds of difference lists
discussed before.
• So we have the best of both worlds:
– a nice simple notation for working with
– the efficiency of difference lists
DCGs
• To see what Prolog translates DCG rules
into:
– let Prolog consult the rules of this DCG, then if
you pose the query:
listing(s)
– you will get the response:
s(A,B) :np(A,C),
vp(C,B).
• This is what Prolog has translated
s --> np,vp into.
• Note that this is exactly the difference list
rule we used in the recognizer.
DCGs
• Similarly, if you pose the query:
listing(np)
• you will get:
np(A,B) :det(A,C),
n(C,B).
• This is what Prolog has translated
np --> det,n into.
• Again (apart from the choice of variables)
this is the difference list rule we used in
the recognizer.
DCGs
• To get a complete listing of the
translations of all the rules, simply type:
listing.
Separating rules and lexicon
• By separating rules and lexicon we mean that we
want to eliminate all mentioning of individual words
in the DCGs and instead record all the information
about individual words separately in a lexicon.
• To see what is meant by this, let's return to the
basic grammar, namely:
np - - > det, n.
vp - - > v, np.
vp - - > v.
det - - > [the].
det - - > [a].
n - - > [woman].
n - - > [man].
v - - > [shoots].
Separating rules and lexicon
• We are going to separate the rules form
the lexicon.
• That is, we are going to write a DCG that
generates exactly the same language,
but in which no rule mentions any
individual word.
• All the information about individual words
will be recorded separately.
Separating rules and lexicon
• Here is an example of a (very simple)
lexicon.
• Lexical entries are encoded by using a
predicate lex/2 whose first argument is a
word, and whose second argument is a
syntactic category:
lex(the, det).
lex(a, det).
lex(woman, n).
lex(man, n).
lex(shoots, v).
Separating rules and lexicon
• A simple grammar that could go with this
lexicon will be very similar to the basic
DCG.
• In fact, both grammars generate exactly
the same language.
• The only rules that change are those that
mention specific words, i.e. the det, n,
and v rules.
det --> [Word], {lex(Word, det)}.
n --> [Word], {lex(Word, n)}.
v --> [Word], {lex(Word, v)}.
Separating rules and lexicon
Grammar:
np - - > det, n.
vp - - > v, np.
vp - - > v.
det --> [Word], {lex(Word, det)}.
n --> [Word], {lex(Word, n)}.
v --> [Word], {lex(Word, v)}.
Separating rules and lexicon
• Consider the new det rule:
det --> [Word], {lex(Word, det)}.
• This rule says “a det can consist of a list
containing a single element Word” (note
that Word is a variable).
• The extra test adds the crucial condition:
“as long as Word matches with
something that is listed in the lexicon as
a determiner”.
Separating rules and lexicon
• With our present lexicon, this means that
Word must be matched either with the
word “a” or “the”:
lex(the, det).
lex(a, det).
• So this single rule replaces the two
previous DCG rules for det.
Separating rules and lexicon
• This explains the how of separating rules
from lexicon, but it doesn't explain the
why.
• Is it really so important?
• Is this new way of writing DCGs really
that much better?
Separating rules and lexicon
• The answer is yes! for a theoretical reason:
– Arguably rules should not mention specific lexical
items.
– The purpose of rules is to list general syntactic facts,
such as the fact that a sentence can be made up of a
noun phrase followed by a verb phrase.
– The rules for s, np, and vp describe such general
syntactic facts, but the old rules for det, n, and v don't.
– Instead, the old rules simply list particular facts: that a
is a determiner, that the is a determiner, and so on.
– From a theoretical perspective it is much neater to
have a single rule that says “anything is a determiner
(or a noun, or a verb,...) if it is listed as such in the
lexicon”.
Separating rules and lexicon
• Now, our little lexicon, with its simple lex
entries, is a toy.
• But a real lexicon is (most emphatically!)
not.
• A real lexicon is likely to be very large (it
may contain hundreds of thousands, or
even millions, of words) and moreover,
the information associated with each
word is likely to be very rich.
Separating rules and lexicon
• Our lex entries give only the syntactical
category of each word.
• A real lexicon will give much more, such as
information about its phonological,
morphological, semantic, and pragmatic
properties.
• Because real lexicons are big and complex,
from a software engineering perspective it is
best to write simple grammars that have a
well-defined way of pulling out the
information they need from vast lexicons.
Separating rules and lexicon
• That is, grammars should be thought of
as separate entities which can access
the information contained in lexicons.
• We can then use specialized
mechanisms for efficiently storing the
lexicon and retrieving data from it.
• The new rules really do just list general
syntactic facts, and the extra tests act
as an interface to our (admittedly simple)
lexicon that lets the rules find exactly the
information they need.
Grammar 1: a trivial grammar
for a fragment of language
s  np, vp.
% A sentence (s) is a noun
phrase (np) plus a verb phrase (vp)
np  det, n.
% A noun phrase is a
determiner plus a noun
np  n.
% ... or just a noun.
vp  v, np.
% A verb phrase is a verb
and its direct object, which is an np
vp  v.
% ... or just the verb (for
intransitives).
det  [Word], {lex(Word, det)}.
n  [Word], {lex(Word, n)}.
v  [Word], {lex(Word, v)}.
Grammar 1: a trivial grammar
for a fragment of language
lex(the, det). % ‘the’ is a determiner
lex(mary, n).
% ‘mary’ is a noun.
lex(john, n).
lex(woman, n).
lex(apple, n).
lex(man, n).
lex(loves, v).
% ‘loves’ is a verb.
lex(eats, v).
lex(sings, v).
Sentences for Grammar 1
•
•
•
•
mary loves john
the woman eats the apple
the man sings
mary eats
Grammar 2: restrictions in
argument selection
s  np, vp.
compl([ ])  [ ].
compl([arg(X)])  p(X), np.
compl([ ])  np.
np  name.
np  det, n.
vp  v(X), compl(X). % A vp is a verb
plus a verbal complement (compl)
Grammar 2: restrictions in
argument selection
v(A)  [Word], {lex(Word, v, A)}.
name  [Word], {lex(Word, name)}.
n  [Word], {lex(Word, n)}.
det  [Word], {lex(Word, det)}.
p(Word)  [Word], {lex(Word, p)}.
Grammar 2: restrictions in
argument selection
lex(piensa, v, [arg(en)]).
lex(está, v, [arg(en)]).
lex(ríe, v, [ ]).
lex(habla, v, [arg(con)]).
lex(lee, v, [ ]).
lex(el, det).
% ‘el’ is a
determiner
Grammar 2: restrictions in
argument selection
lex(un, det).
lex(mary, name).
lex(john, name).
lex(profesor, n).
lex(en, p)
Sentences for Grammar 2
•
•
•
•
mary piensa en john
john habla con mary
john ríe
un profesor habla con mary
Extension of Grammar 2
John habla de Clara con Mary
• Needed modifications:
compl([arg(X) | Y])  p(X), np, compl(Y).
lex(habla, v, [arg(de), arg(con)]).
lex(clara, name).
Grammar 3: logical
representation of sentences
s(F)  np(S), v(S, X, F), compl(X).
compl([ ])  [ ].
compl([arg(X,O) | Y])  p(X), np (O),
compl(Y).
compl([arg(null, O) | Y])  np(O),
compl(Y).
np(S)  name(S).
np(S)  det, n(S).
Grammar 3: logical
representation of sentences
v(S,A,F)  [Word], {lex(Word, v, S, A, F)}.
name(Word)  [Word], {lex(Word, name)}.
n(Word)  [Word], {lex(Word, n)}.
det  [Word], {lex(Word, det)}.
p(Word)  [Word], {lex(Word, p)}.
Grammar 3: logical
representation of sentences
lex(clara, name).
lex(maria, name).
lex(juan, name).
lex(barcelona, name).
lex(libro, n).
lex(hombre, n).
lex(profesor, n).
Grammar 3: logical
representation of sentences
lex(el, det).
lex(un, det).
lex(en, p).
lex(con, p).
lex(de, p).
Grammar 3: logical
representation of sentences
lex(ríe, v, S, [ ], reir(S)).
lex(piensa, v, S, [arg(en, O)], pensar_en(S, O)).
lex(habla, v, S, [arg(de, O),arg(con, O1)], comunica(S,O,
O1)).
lex(habla, v, S, [arg(con, O),arg(de, O1)],
comunica(S,O1, O)).
lex(está, v, S, [arg(en, O)], locativo(S, O)).
lex(lee, v, S, [arg(null, O)], leer(S, O)).
Sentences for Grammar 3
• unary predicate (ríe, v, S, [ ], reir(S)).
• binary predicate (piensa, v, S, [arg(en, O)],
pensar_en(S, O)).
• ternary predicate (habla, v, S, [arg(con,O),
arg(de, O1)], comunica(S, O1, O)).
• Example:
Juan piensa en Maria = pensar_en(juan, maria).
Prolog input and output
analysis(F, X, [ ]):- s(F, X, [ ]).
| ?- analysis(F, [juan, está, en, barcelona], [ ]).
F = locativo(juan, barcelona) ?
yes
| ?- analysis(F, [juan, piensa, en, maria], [ ]).
F = pensar_en(juan, maria) ?
yes
Prolog input and output
| ?- analysis(F, [el, libro, está, en, barcelona], [ ]).
F = locativo(libro, barcelona) ?
yes
| ?- analysis(F, [juan, lee, un, libro], [ ]).
F = leer(juan, libro) ?
yes
Prolog input and output
| ?- analysis(F, [el, hombre, habla, de, juan, con, maria], [ ]).
F = comunica(hombre, juan, maria) ?
yes
| ?- analysis(F, [el, hombre, ríe], [ ]).
F = reir(hombre) ?
yes
Prolog input and output
| ?- analysis(F, [el, profesor, piensa, en, un, libro], [ ]).
F = pensar_en(profesor, libro) ?
yes
Grammar 4: quantification
• It exists X and X is a libro:
el libro = e(X, libro(X)).
• All X such that X is a libro:
todo libro = a(X, libro(X)).
Grammar 4: quantification
el libro cae = e(X, and(libro(X), cae(X)))
Juan piensa en el libro = e(X, and(libro(X),
piensa(juan, X)))
todo hombre piensa en el libro = a(X,
implies(hombre(X), e(Y, and(libro(Y),
piensa(X,Y)))
Grammar 4: quantification
lex(el,det,K,S1,S2,e(K,and(S1,S2))).
lex(un,det,K,S1,S2,e(K,and(S1,S2))).
lex(los,det,K,S1,S2,a(K,implies(S1,S2))).
lex(todo,det,K,S1,S2,a(K,implies(S1,S2))).
np(K,S2,F)  det(K,S1,S2,F), n(K,S1).
np(K,F,F)  name(K).
Grammar 4: quantification
compl([ ],S,S)  [ ].
compl([arg(X,K) | Y],S1,S)  p(X),
np(K,S2,S), compl(Y,S1,S2).
s(S)  np(K,S2,S), v(K,X,S1),
compl(X,S1,S2).
n(K,F)  [Word],{lex(Word,n,K,F)}.
lex(libro,n,K,libro(K)).
Prolog input and output
| ?- analysis(F,[el,hombre,ríe],[ ]).
F = e(_A,and(hombre(_A),reir(_A))) ?
yes
| ?- analysis(F,[el,profesor,piensa,en,un,libro],[ ]).
F = e(_B,and(profesor(_B),e(_A,and(libro(_A),pensar_en(_B,_A))))) ?
yes
Prolog input and output
| ?- analysis(F,[el,hombre,habla,de,juan,con,maria],[ ]).
F = e(_A,and(hombre(_A),comunica(_A,juan,maria))) ?
yes
| ?- analysis(F,[todo,hombre,piensa,en,un,libro],[ ]).
F = a(_B,implies(hombre(_B),e(_A,and(libro(_A),pensar_en(_B,_A))))) ?
yes
Prolog input and output
| ?- analysis(F,[todo,libro,esta,en,barcelona],[ ]).
F = a(_A,implies(libro(_A),locativo(_A,barcelona))) ?
yes
Extension of Grammar 4
El hombre bueno:
e(X, and(hombre(X), bueno(X)))
Grammar 5: semantic
constraints
• Argument selection:
– *Juan lee el hombre
– El gato come pescado
– El perro corre por el camino
• Semantic categories:
– human: Juan, María, Clara, hombre, profesor
– animate: perro, gato
– inanimate: libro, pescado, bocadillo, silla
– locative: Barcelona, camino
Nouns’ semantic categories
lex(clara, name, human).
lex(maria, name, human).
lex(juan, name, human).
lex(barcelona, name, locative).
Nouns’ semantic categories
lex(libro, n, K, libro(K), inanimate).
lex(hombre, n, K, hombre(K), human).
lex(profesor, n, K, profesor(K), human).
lex(perro, n, K, perro(K), animate).
lex(gato, n, K, gato(K), animate).
lex(camino, n, K, camino(K), locative).
Verbs’ semantic categories
lex(piensa, v, S, [arg(en,O)],
pensar_en(S,O), sem(human, [X])).
lex(habla, v, S, [arg(de,O),arg(con,O1)],
comunica(S,O,O1), sem(human,
[X,human])).
lex(está, v, S, [arg(en,O)], locative(S,O),
sem(X, [locative])).
lex(lee, v, S, [arg(null,O)], leer(S,O),
sem(human, [inanimate])).
Grammar 5: semantic
constraints
v(S,A,F,sem)  [Word],{lex(Word,v,S,A,F,sem)}.
name(Word,sem) 
[Word],{lex(Word,name,sem)}.
n(Word,sem)  [Word],{lex(Word,n,sem)}.
np(K,S2,F,sem)  det(K,S1,S2,F), n(K,S1,sem).
np(K,F,F,sem)  name(K,sem).
Grammar 5: semantic
constraints
compl([ ],S,S,[ ])  [ ].
compl([arg(X,K) | Y],S1,S,[sem | sem2])  p(X),
np(K,S2,S,sem), compl(Y,S1,S2,sem2).
s(S)  np(K,S2,S,sem1),
v(K,X,S1,sem(sem1,list-sem)),
compl(X,S1,S2,[list-sem]).