Spring 2012
Juyeon Kang
qkang@fi.muni.cz
B410, Faculty of Informatics, Masaryk University,
Brno, Czech Rep.
IA165
Combinatory Logic for
Computational Semantics
Summing up: last lecture
● How to apply the combinators to natural language analysis
1) using introduction and elimination rules by beta-reduction of1) using introduction and elimination rules by beta-reduction of
combinators: control heurstic of combinatorial application andcombinators: control heurstic of combinatorial application and
bracketingbracketing
2) using a syntactic tool for controlling the application of combinators
: CCG assumes the preliminary steps to find a well-structured normal
form, that is, a formal semantic structure
Remind...
● Combinator W
: The combinator W takes one functor f and applies the functor f to
the argument x by duplicating the argument x. → duplication
Intro. and Elim. Rules of the combinator W
Short introduction to ”Reflexivization”-1
● In binding theory (P.Schlenker, UCLA, presented in ESSLLI04’)
”Conditions of acceptance of the reflexivization”
Condition A: A reflexive (or reciprocal) pronoun must be bound within
its local domain.
a. John1
likes himself1
b. *[John1
’s mother]2
likes himself1
c.*John1
thinks that Mary2
likes himself1
Condition B: A non-reflexive pronoun must be free (cannot be
bound) within its local domain.
a. *John1
likes him1
b. [John’s mother]2
likes him1
c. John1
thinks that Mary2
likes him1
Condition C: An R-expression (=proper noun) must be free.
a. ??John1
likes John1
(*He1
likes John1
)
b. [John1
’s mother]2
likes John1
c. ??John1
thinks that Mary2
likes John1
Mary thinks that Mary is clever is ”interpretable”
however it is ruled out on pragmatic ground because there is
a ’better’ logical form to express the same meaning, namely
Mary thinks that she is clever
Mary thinks that Mary is clever is ”interpretable”
however it is ruled out on pragmatic ground because there is
a ’better’ logical form to express the same meaning, namely
Mary thinks that she is clever
● Counter-example of the condition A
English reflexives have logophoric homonyms that are pronominal
example:
Alberti
 was upset that Mary had endangered Gordon and himselfi
 on the climbing 
trip.
Formal semantic analysis of the ”Reflexivization”
● the pronoun itself, like all noun phrases, is type-raised
==> (operator SELF).
● Unlike most arguments, it is a clitic, like French (and Czech) se, which
means that it is specialized to apply only to lexical verbal categories.
The natural way to capture this specialization is to define it as a
”lexicon-internal morphological operator”
(sentences given by Johan van Benthem, Computational Linguistics and Formal
Semantics)
● Example : Reflexives I
1. Mary despised herself
2. ?Maryi
 despised Maryi
3. John despised Anna
1’. DESPISE(ONESELF)(MARY)
2’. DESPISE (MARY)(MARY)
3’. DESPISE (ANNA)(JOHN)
1’. DESPISE(ONESELF)(MARY)
2’. DESPISE (MARY)(MARY)
3’. DESPISE (ANNA)(JOHN)
● Mary despised herself
Definition of the operator ”SELF”
: is an operator which operates on the binary predicate despise to form
the unary predicate ”SELF­despise”
Important remark:
The paraphrase of the Mary despised herself is Mary despise Mary, that is,
”one has an acitivity to despise and it is Mary who is this person”.
herself =def
 SELFherself =def
 SELF
1/ Mary despised herself
2/C*Mary despised herself Hypothesis 1 [C*Mary=Mary]
3/C*Mary SELF despised1
Hypothesis 2 [P2
SELF =def
SELF P1
]
4/C*Mary W despised1
Hypothesis 3 [SELF=W]
4/B(C*Mary W)despised1
Intro. Of B
5/(C*Mary) (W despised1
) Elim. Of B
6/(W despised1
)Mary Elim. Of C*
7/ (despised1
)Mary Mary Elim. Of W
P2
 SELF =def
 SELF P1
P2
 SELF =def
 SELF P1
1/ ((herself)despisedP1
)Mary
2/((SELF)despised)Mary Hypothesis 1 [herself=SELF]
3/(W despised )Mary Hypothesis 2 [SELF=W]
4/(despised (Mary))Mary Elim. Of W
SELF =def
 WSELF =def
 W
Reflexive-marked predicate: ’seem’ and ’believe’
● Condition A: A reflexive-marked predicate must be semantically
reflexive.
● Condition B: A semantically reflexive predicate must be reflexive-
marked.
Conditions A and B effect beyond the domain of the predicate.
a. John seems to himself to be sick.
a’. seems to himself [John to be sick]
b. John believes himself to be sick
b’. John believes [himself to be sick]
a’. seems to himself [John to be sick]
b’. John believes [himself to be sick]
there appears to be a relation of ”reflexivization”
between a semantic argument of the embedded clause
and a semantic argument of the matrix verb.
John believes himself to be sick
C*John REF believes to­be­sick
==> [C*John’=John] [himself=SELF] [SELF=REF]
B(B(C*John’ REF)believes)to­be­sick
(C*John’)(W(believes(to­be­sick)))
==> [REF=W]
(believes(to­be­sick)John) John
Multilingual examples of Reflexives-1
● French
1. Jean se rase (John SE shaves)
2. Jean rase lui­meme (John shaves HIMSELF)
3. ?Jeani
 rase Jeani 
(John shaves JOHN)
4. Le coiffeur rase Pierre (The barber shaves Pierre)
1’. (SE RASE)JEAN
2’. RASE(LUI­MEME)JEAN
3’. RASE (JEAN)(JEAN)
4’. RASE PIERRE (LE COIFFEUR)
1’. (SE RASE)JEAN
2’. RASE(LUI­MEME)JEAN
3’. RASE (JEAN)(JEAN)
4’. RASE PIERRE (LE COIFFEUR)
● Jean se rase ≈ Jean rase Jean
Definition of the operator ”REF”
: is an operator which operates on the binary predicate rase to form a
unary predicate ”REF-rase”
Question.
How to explain the paraphrastic relation between Jean se rase and *Jean
rase Jean?
Possibility: consider the reflexive se as the linguistic trace of the
combinator W
● Law of the reflexivization
1/Jean se rase
2/C*Jean se rase Hypothesis 1 [Jean=C*Jean]
3/C*Jean REF rase Hypothesis 2 [REF=se]
4/C*Jean W rase Law of Reflex. [REF=W]
5/B(C*Jean W) rase Intro. Of B
6/ (C*Jean) (W rase) Elim. Of B
7/ (W rase)Jean Elim. Of C*
8/ (rase(Jean)) Jean Elim. Of W
[REF]  [REF =def
  W][REF]  [REF =def
  W]
Multilingual examples of Reflexives-2
● Czech
Marie slyšela Petra mluvit.  Marie se slyšela mluvit (v rádiu).
Mary heard Peter­Acc speak­Inf.  Mary SE heard speak­Inf (in a radio).
‘Mary heard Peter speaking.’  ‘Mary heard herself speaking (in a radio)’
≈ Mary heard that Peter is speaking ≈ Mary heard that Mary is speaking
(Slyšela (Petra(mluvit)))Marie (Slyšela (Marie(mluvit)))Marie
● Definition of the operator ”REF”
: is an operator which operates on the binary predicate slyšela to
form a unary predicate REF-slyšela
Definition1 
[REF=se]
Definition1 
[REF=se]
Definition 2
[REF]  [REF =def
  W]
The reflexive ”se” is a linguistic 
trace of the combinator W
Definition 2
[REF]  [REF =def
  W]
The reflexive ”se” is a linguistic 
trace of the combinator W
Marie slyšela Petra mluvit
1/Marie slyšela Petra mluvit
2/C*Marie slyšela Petra mluvit Intro of C*
3/(B(C*Marie) slyšela) Petra mluvit Intro of B
4/(B(B(C*Marie) slyšela) Petra) mluvit Intro of B
5/((B(C*Marie) slyšela) (Petra mluvit)) Elim. Of B
6/(C*Marie) (slyšela (Petra mluvit)) Elim. Of B
7/(slyšela (Petra mluvit))(Marie)  Elim. Of C*
Marie se slyšela mluvit (v rádiu)
1/Marie se slyšela mluvit
2/C*Marie se slyšela mluvit Hypothesis 1 [C*Marie=Marie]
3/C*Marie REF slyšela mluvit Hypothesis 2 [REF=se]
4/B((C*Marie) REF) slyšela mluvit Intro of B
5/B(B((C*Marie) REF) slyšela) mluvit Intro of B
6/B(B((C*Marie) W) slyšela) mluvit Hypothesis 3 [REF=W]
7/B((C*Marie) W) (slyšela mluvit) Elim of B
8/(C*Marie) (W (slyšela mluvit)) Elim of B
9/ (W (slyšela mluvit))(Marie) Elim of C*
10/ ((slyšela mluvit)(Marie))(Marie) Elim of W
23
Next week...
● Continue about the application of the combinators to natural
language analysis: passivization