Spring 2012
Juyeon Kang
qkang@fi.muni.cz
B410, Faculty of Informatics, Masaryk University,
Brno, Czech Rep.
IA165
Combinatory Logic for
Computational Semantics
Some Tools
● https://files.nyu.edu/cb125/public/Lambda/ski.html (Chris Barker)
➢ S-K-I proofness checking
● http://www.angelfire.com/tx4/cus/combinator/birds.html (Chris Rathman)
➢ elementary combinators calculator
● http://svn.ask.it.usyd.edu.au/trac/candc/wiki/Demo (Johan Bos)
➢ based on the DRT (generation of the DRS)
➢ Boxing: process of turning real texts into the
box-like semantic representation used in DRT
➢ http://homepages.inf.ed.ac.uk/jbos/comsem/book2.html
Summing up-1
● Combinators
➢ elementary combinators: B, C, W, C*, Φ ...
➢ derived combinators
➢ Deferred combinators: B2
, C3
...
➢ Powers of combinators:B3
, C2
...
==> Remind the beta-reduction rules of each combinator
Summing up-2
1. Reflexivisation: the operator SELF
2.Passivisation: the operator PASS
3. Aspecto-temporal relation: the operators STATE, PROC, EVENT
4. Quantification: the operators Π and Σ
1. Reflexivisation
Mary despised herselfherself
herself =def
 SELFherself =def
 SELF
P2
 SELF =def
 SELF P1
P2
 SELF =def
 SELF P1
SELF =def
 WSELF =def
 W
Mary despised MaryMary
2. Passivisation-1
The man has been killed by the enemy
↓
The enemy has killed the man
The man has been killed by the enemy
↓
The enemy has killed the man
[PASS = B   C ]Σ[PASS = B   C ]Σ
(EΣ 1
 E2
)   (E→ 1
 x E2
)(EΣ 1
 E2
)   (E→ 1
 x E2
)
Passivisation-2
The lexical predicate “give­to” has a predicate converse
associated to “receive­from”;
[receive­from z y x = give­to x y z]
The lexical predicate “give­to” has a predicate converse
associated to “receive­from”;
[receive­from z y x = give­to x y z]
 [ give­to = BC (C (BC (receive­from))) ] [ give­to = BC (C (BC (receive­from))) ]
PROCJ0
 ((I­SAY) (& (ASPI
 ( )) [I REP JΛ 0
]))
comment:
the aspectual process PROCJ0
 is applied on the result of the application of (I­
SAY) on a conjunction of an aspectualized predicative relation ASPI
 ( )  and a Λ
temporal relation [I REP J0
] between the interval I related to the predicative 
relation and an interval J0
 related to enunciative process.
PROCJ0
 ((I­SAY) (& (ASPI
 ( )) [I REP JΛ 0
]))
comment:
the aspectual process PROCJ0
 is applied on the result of the application of (I­
SAY) on a conjunction of an aspectualized predicative relation ASPI
 ( )  and a Λ
temporal relation [I REP J0
] between the interval I related to the predicative 
relation and an interval J0
 related to enunciative process.
3. Aspecto-temporal relation-1
Aspecto-temporal relation-2
● Operators of the aspectuality
a. COMPLETE-EVENT-PAST: e.g. Verbal ending -ed
 [COMPLETE­EVENT­PAST=X & ([ (Fδ 4
) <  (Jδ 0
)]) I­am­saying EVENF4
]
where X is  B6
C3
C3
CB2
b. INC-PRST: verbal ending -e
[INC_PRST J1
 J0
 =déf B2
 (C2
 B) B2
 I­am­sayingJ0
 & PROCJ1
 ([ (Jδ 1
)= (Jδ y
)])] 
4. Quantification
● Theories of quantification
a. Fregean teories with bound variables
1. Classical theory in First­Order Language
2. Montague’s quantification expressed in Church’s λ­Calculus
b. Fregean theory without bound variables 
3. Illative theory expressed in Curry’s Combinatory Logic
a. Fregean teories with bound variables
1. Classical theory in First­Order Language
2. Montague’s quantification expressed in Church’s λ­Calculus
b. Fregean theory without bound variables 
3. Illative theory expressed in Curry’s Combinatory Logic
● Illative universal quantifiers: Π1
and Π2
● Illative existential quantifiers: Σ1
and Σ2
Definition of the universal quantifier
[ Π2
 =def
 ((B(CB2
) ) => Φ Π1
) ]
Definition of the universal quantifier
[ Π2
 =def
 ((B(CB2
) ) => Φ Π1
) ]
Definition of the existential quantifier
[ Σ2
=def
(B(CB2
)Φ) & Σ1
]
Definition of the existential quantifier
[ Σ2
=def
(B(CB2
)Φ) & Σ1
]
Text analysis using combinators
● ...Max opened the door. The room was pitch dark. He so switched on 
the light. John was waiting there. When John greeted him, Max felt 
a shrap pain from his back....
● ...Anna is drawing herself in front of a mirror. The deadline is 
announced by the teacher.  All students should finish it fast. But 
some may need more times...
Open­ed
EVENT
was
STATE
switch­ed
EVENT
was­ing
PROC
greet­ed
EVENT
felt
EVENT
is­ing
PROC
SELF
Reflexe
SELF
Reflexie
PASS
Passivisation
Π
Quantification
Σ
Quantification
13
Next week...
● Course Examination on 25 May 2012
– from 2pm-4pm
– B410
– Any materials are allowed