Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
Classwork N°7
due to 13th April 2012
Exercise: “Application of combinators to natural language analysis: Reflexivization”
1. To apply successfully the combinators to natural language analysis, we need to handle
adequately the introduction and elimination rules by beta-reduction defined for each
combinator. Please remind these rules and apply them to the following sentences.
Wfx  →β  fxx 
(a) John sent himself a letter
Hypothesis
[John=C*John’][himself=SELF] [P3 SELF=SELF P2] [SELF= W]
1/C*John sent SELF a letter
2/B(C*John) sent SELF a letter
3/(B(C*John) SELF) sent a letter
4/(B(B(C*John) SELF) sent) a letter
5/(B(C*John) SELF) (sent (a letter))
6/(C*John) (SELF (sent (a letter)))
7/(SELF (sent (a letter)))(John)
8/(W (sent (a letter)))(John)
9/(sent (a letter))(John)(John)
(b) The fixed-point theorem proved itself
Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
Hypothesis
[P2 SELF=SELF P1]
[the-fixed-point-theorem=C*the-fixed-point-theorem’][itself=SELF] [SELF= W]
d) He found himself qualified
Hypothesis
[he=C*he’][himself=SELF] [SELF= W] [P2 SELF=SELF P1]
1/C*he’ found SELF qualified
2/C*he’ SELF found’ qualified
2/B(C*he’ SELF) found’ qualified
3/B(B(C*he’ SELF)found’) qualified
4/B(C*he’ SELF) (found’ qualified)
5/(C*he’) (SELF (found’ qualified))
6/(SELF (found’ qualified))(he)
7/(W (found’ qualified))(he)
8/(found’ qualified)(he)(he)
(d) Mary heard herself speaking (in a radio)
Hypothesis
[Mary=C*Mary’][herself=SELF] [SELF= W] [P2 SELF=SELF P1]
1/C*Mary’ heard SELF speaking
2/C*Mary’ SELF heard’ speaking
2/B(C*Mary’ SELF) heard’ speaking
3/B(B(C*Mary’ SELF)heard’) speaking
4/B(C*Mary’ SELF) (heard’ speaking)
5/(C*Mary’) (SELF (heard’ speaking))
6/(SELF (heard’ speaking))(Mary)
Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
7/(W (heard’ speaking))(Mary)
8/(heard’ speaking)(Mary)(Mary)
2. Formal semantic analysis of Reflexives using combinators: “Multilingual examples”
(e) a. Marie se viděla tančit (v zrcadle) (Mary saw herself dance (in a mirror))
Hypothesis
[Marie=C*Marie’][se=REF] [REF= W]
1/C*Marie’ REF viděla tančit
2/B(C*Marie’ REF) viděla tančit
3/B(B(C*Marie’ REF) viděla) tančit
4/B(C*Marie’ REF) (viděla tančit)
5/C*Marie’ (REF (viděla tančit))
6/C*Marie’ (W (viděla tančit))
7/(W(viděla tančit))(Marie)
8/(viděla tančit)(Marie)(Marie) =Mary saw that Mary dance
b. Marie viděla Petra tančit (Mary saw Peter dance)
Hypothesis
[Marie=C*Marie’]
1/C*Marie’ viděla Petra tančit
2/B(C*Marie’ viděla) Petra tančit
3/B(B(C*Marie’ viděla) Petra )tančit
4/B(C*Marie’ viděla) (Petra tančit)
5/C*Marie’ (viděla (Petra tančit))
6/ (viděla (Petra tančit))Marie =Mary saw that Peter dance
(f) a. Soudce se shledal vinným (The judge found himself guilty)
Hypothesis
Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
[Soudce=C*Soudce’][se=REF] [REF= W]
1/C*Soudce’ REF shledal vinným
2/B(C*Soudce’ REF) shledal vinným
3/B(B(C*Soudce’ REF) shledal) vinným
4/B(C*Soudce’ REF) ( shledal vinným)
5/C*Soudce’ (REF ( shledal vinným))
6/C*Soudce’ (W ( shledal vinným))
7/(W( shledal vinným))(Soudce)
8/( shledal vinným)(Soudce)(Soudce) = the judge found that he is guilty
b. Soudce shledal Petra vinným. (The judge found Peter guilty)
Hypothesis
[Soudce=C*Soudce’]
1/C*Soudce’ shledal Petra vinným
2/B(C*Soudce’ shledal) Petra vinným
3/B(B(C*Soudce’ shledal) Petra ) vinným
4/B(C*Soudce’ shledal) (Petra vinným)
5/C*Soudce’ ( shledal (Petra vinným))
6/ ( shledal (Petra vinným)) Soudce =the judge found that Peter is guilty
(g) a. Jean se lave (Jean washes himself)
Hypothesis
[Jean=C*Jean’][se=REF] [REF= W]
1/C*Jean’ REF lave
2/B(C*Jean’ REF) lave
3/C*Jean’ (REF lave)
4/(REF lave)Jean
5/ (lave)Jean Jean
Spring 2012 IA165 Combinatory Logic for Computational Semantics by Juyeon Kang
b. Jean lave son assiette (Jean washes his dish)
Hypothesis
[Jean=C*Jean’]
1/C*Jean’ lave son assiette
2/B(C*Jean’lave) son assiette
3/B(B(C*Jean’lave) son) assiette
4/B(C*Jean’lave) (son assiette)
5/C*Jean’(lave (son assiette))
6/(lave (son assiette))Jean