An introduction to ANAPHORA and
Quantification
Syntax and Interpretation
Genève, 2010
Two conceptions of semantics
1.
Morris 1938: canonical division into syntax,
semantics and pragmatics. According to this view,
semantics is concerned with the relationship
among linguistic expressions and
objects/individuals of the world
2.
Conceptual semantics (Jackendoff): semantics is
concerned with a special kind of
expressions/representations that characterize a
specific status of the mind/brain
Chomsky: semantics does not involve a
direct relation with the external world
Criticism of the notion of reference: linguistic expressions
refer to the objects of the world, but this happens “from the
perspective of specific human interests and objectives, and
with curious properties” (Nuovi orizzonti, 73). “…un’unità
lessicale ci fornisce una certa gamma di prospettive per
guardare a quelli che consideriamo oggetti del mondo, o che
concepiamo in modi diversi; queste unità lessicali sono come
filtri o lenti che ci mettono a disposizione modi per guardare
alle cose e pensare ai prodotti della nostra mente. I termini
stessi non hanno riferimento, perlomeno se il termine
riferimento è utilizzato con il senso che ha nel linguaggio
naturale; ma le persone possono utilizzare i termini per
riferirsi alle cose, guardandole da particolari punti di vista (i
quali, come si è già osservato, sono assai lontani dalla
prospettiva adottata nelle scienze naturali (95)
Some examples to show that the notion of
“reference” is problematic
1.
Il libro che sto scrivendo peserà almeno 5 chili se
sarà mai pubblicato
2.
London is so unhappy, ugly, and polluted that it
should be destroyed and rebuilt 100 miles away
3.
John is painting the house brown
4.
Se vedo una casa, vedo la superficie esterna; se
sono in un aereo, lo vedo solo se guardo fuori dal
finestrino e vedo la superficie dell’ala (94)
The nature of semantic computations
1.
Chomsky: Semantic representations are part of
syntax and consist in the manipulation of symbolic
objects.
1.
The point of view that I will take:
Semantic computations are distinct from syntactic
computations and involve the use of a set-theoretic
apparatus that relates linguistic expressions to
objects in a model. What counts here are the
logical and mathematical properties of those
objects whereas the non-formal properties are
disregarded.
Semantic computations and pronominal
anaphora
1.
Pronouns as bound variables: the
constraints on pronominal anaphora
are NOT constraints on coreference
2.
Semantics and language acquisition:
Delay in the acquisition of Principle B
of Binding Theory
Bound variables readings
(1)
(2)
Every student thinks that Mary likes him
x (x thinks that Mary likes x)
(3)
(4)
The professor who tested every student thinks that Mary likes him
*x (the professor who tested x thinks che Mary likes x
(5)
(6)
The professor who tested no student thinks that Mary likes him
*x (the professor who did not test x thinks that Mary likes x)
(7)
The professor who did not test Charles thinks that Mary likes him
(8)
(9)
The professor who tested him thinks that Mary likes no student
*x (the professor who tested x thinks thatMary does not like x)
(10)
The professor who tested him thinks that Mary does not like Charles
CONCLUSIONE: C-command is relevant for bound variable readings, but
is irrelevant for coreference
Properties and functions
¶Tito sleeps¶
The interpretation takes place according to a certan
number of parameters (time, assignment function,
world, etc.)
¶Tito¶ = t
¶sleeps¶ = [a, b, c, d…]
Sleeps (x) = V/F
x [x  sleep’]
x [x  sleep’] (t) = [t  sleep’]
Semantic tipes
f <e,t> = properties (N, V, A)
 f <e,e> = mother of
 f <t,t> = negation
 f <e, <e,t>> = transitive verbs
 f <<e,t>, <e,t>> = antonyms,
modifiers…
 f <<e,t>, t> = quantifiers

Individuals as set of properties
x y P [[P(x)  P(y)]  x = y]
 x y P [ x = y  [P(x)  P(y)]

¶Tito¶ = P<e,t> [t  P]
¶Tito sleeps¶ = 1 iff ¶Tito¶  ¶sleeps¶
¶Tito sleeps¶ = 1 iff ¶sleeps¶  ¶Tito¶
Quantifiers
1.
2.
3.
4.
5.
6.
7.
8.
Every soldier dreamed
Some soldier dreamed
No soldier dreamed
x [soldier’(x)  dreamed’(x)]
x [soldier’(x)  dreamed’(x)]
x [soldier’(x)  dreamed’(x)]
[[every soldier] dreamed]
[every [soldier dreamed]]
Generalized quantifiers
1. ¶every soldier¶ = P<e,t> [soldier’  P]
2. ¶some soldier¶ = P<e,t> [soldier’  P  ]
3. ¶no soldier¶ = P<e,t> [soldier’  P = ]
¶every soldier sleeps¶ = ¶every soldier¶ (¶sleeps¶)
P<e,t> [soldier’  P] <<e,t>, t> (sleeps’ <e,t>) = soldier’  sleeps
[ [every? soldier<e,t>]<<e,t>,t> sleeps<e,t>]
5. ¶every¶ = PQ [P  Q]
6. ¶some¶ = PQ [P  Q  ]
7. ¶no¶ = PQ [P  Q = ]
Exercises
1.
Express 1-3 (previous slide) in terms of
first-order logic notation
2.
Give the semantics of “exactly two”
3.
Give the semantics of “most”
C-command and coreference
Every student likes him
(2)
Charles loves him
QUESTION: Is Principle B a constraint on BINDING or a constraint on
COREFERENCE?
(3) Genève is loved by its inhabitants, Verona is not
(4) Genève [x (x è amata dagli abitanti di x)]
Verona [x (x non è amata dagli abitanti di x)]
(5) The people who live in Geneva love it, but the people who live in
Verona do not
(6) Genève [x (the people living in x love x)]
*Verona [x (the people living in x do not love x)]
CONCLUSIONE: The bound variable reading is possible with proper
names as well. It is then possible that the constraint on (2) concerns
the bound variable reading and NOT coreference
(1)
“Oscar-sentences” and
coreference
(1)
It’s not true that Michael loves nobody!
He loves Michael
(2) It’s not true that nobody likes Michael!
Michael likes him
Crossover and Condition C
(1)
(2)
Who does he like?
Who does his professor like?
(3)
(4)
He loves everyone’s mother
His mother loves everyone
(3)
Someone loves everyone’s mother
QUESTION: Why has the trace of the operator (wh-phrase or quantifier) to ccommand the pronoun?
COROLLARY: Why does semantic binding entails syntactic binding in natural
language?
Syntactic and Semantic binding
 binds  if  c-commands  and  is coindexed with .
Let  be a branching node with daughters  and , where  dominates
only a numerical index i. Then, for every variable assignment g, ||||g =
x. ||||g: i  x

||||g = x. ||||g: i  x
QP
1

t1

…i….
Two ideas of anaphoric dependence
1. CLP: If x depends on y, then y has to c-command x
Under CLP indexes produce only BVRs and coreference is accidental
covaluation.
Grammatical principles (BT principles) express constraints on the BVR.
2. INP: If x depends on y, then x cannot c-command y
Under INP anaphoric dependencies are encoded through an asymmetric
relation of linking. Grammatical principles constrain linking. Covaluation of
two DPs is linking.
3. Both CLP and INP must be supplemented by an Obviation Rule stating that
two DPs that exclude coindexation or linking as a result of grammar cannot be
covalued
(Reinhart’s Rule I and Safir’s Obviation)
4. John saw him
5. John said that he saw him
The delay in the acquisition of Principle B
(Grodzinsky&Reinhart 1993, Baauw&Delfitto 2005)
1.
a. The boy touched him
2.
b. The boy touched himself (almost 100% adult-like)
Every boy touched him
(85% adult-like)
La niña la señala (90% adult-like)
3.
4.
5.
6.
7.
(around 50% adult-like)
a. Do you know what Mary and John have in common? Mary
admires him and John admires him too
Zelda’s husband is him
A. Is this speaker Zelda? B. How can you doubt it? She praises her
to the sky. No competing candidate would do that
It is not really true that everyone likes John. JOHN does not like him!
Clitici pronominali come variabili:
dislocazione a sinistra e familiarità
Questo libro l’ho già letto
1’. Questo libro [x (ho già letto x)]
1.
L’ho già letto
2’. [TOPe] [x (ho già letto x)]
2.
Ognuno pensa che Maria lo ami
3’. Ognuno [x (x pensa che Maria ami x)]
3.
Quantificazione e scope
(2)
Ogni studente legge
OGNI [studente] [legge]
(3)
Leo incontra ogni studente
(1)
Domanda: Qual è il secondo insieme della relazione?
(4)
(5)
(6)
(7)
[Ogni studente] [Leo incontra x]
OGNI [x: studente] [x: Leo incontra x]
Il professore che ha promosso ogni studente è impazzito
*Quale studente il professore che ha promosso è impazzito?
Quantificazione e calcolo
predicativo
(1)
(2)
(3)
(4)
Ogni studente legge
x [studente(x)  legge(x)]
Most students read
Most x [student(x)  read(x)]
Si consideri un modello composto da 10 persone, di cui 6 leggono. Di
queste 10 persone, 5 sono studenti. Dei 5 studenti, 1 legge e 4 non
leggono.
In questo modello, si dimostra che (4) è vera e che (3) è falsa.
Quindi (4) non rappresenta una forma logica adeguata per (3)
Proprietà logiche della
quantificazione
1.
2.
3.
4.
Ogni A = XU/AX
Qualche A = XU/AX
Most A = XU/AXA-X
Nessun A = XU/AX=
ISOMORFISMO: L’interpretazione di D è indifferente alle
permutazioni degli individui di U. I determinanti sono
indifferenti alle proprietà o individui particolari
DOMANDA: Dimostrare che Qualche(A) è B  Qualche(f(A)) è
f(B), indipendentemente dalla caratterizzazione di f
Quantificazione e
conservatività
CONSERVATIVITA’: D(A) è B  D(A) è AB
1.
Qualche uomo corre  Qualche uomo è un uomo che corre
2.
La maggior parte degli uomini corre  La maggior parte degli uomini sono
uomini che corrono
RELAZIONI NON-CONSERVATIVE:
3.
4.
A = B è vero sse A = AB (identità)
<X,Y>: X>Y (quantificatore di Rescher)
5.
6.
Solo gli uomini fumano  solo gli uomini sono uomini che fumano
Solo A è B  AB
Ma SOLO non è un determinante, ha invece la distribuzione di un avverbiale
MONOTONICITA’
(1)
(2)
(3)
(4)
Ogni studente ha lasciato la festa prima delle 10
Ogni studente ha lasciato la festa prima delle 11
Nessuno studente ha lasciato la festa prima delle 10
Nessuno studente ha lasciato la festa prima delle 9
(5)
(6)
*Every student saw any professor
No student saw any professor
(7)
(8)
Every student who praised any professor succeeded
*Every student who succeeded praised any professor
(9)
(10)
Every student who left before 10 passed the exam
Every student who left before 9 passed the exam