Przepiórkowski-inspired Quantification in TRALE Jonathan Khoo jkhoo@sfs.uni-tuebingen.de Grammar Engineering Summer Semester 2006 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 1 / 44
Agenda Background 1 Przepiórkowski 1998 2 Development of the Grammar 3 In Action 4 Summary 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 2 / 44
Agenda Background 1 Przepiórkowski 1998 2 Development of the Grammar 3 In Action 4 Summary 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 3 / 44
Quantifiers and Quantificational NPs Representing quantifiers: every car a car ∀ x ( CAR ( x )) ∃ x ( CAR ( x )) Universal quantification Existential quantification Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 4 / 44
Quantifier Scope Ambiguity A representative visits each customer. There is a different representative for each customer. There is one representative for all customers. Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44
Quantifier Scope Ambiguity A representative visits each customer. There is a different representative for each customer. ∀ y ( CUSTOMER ( y ) → ∃ x ( REPRESENTATIVE ( x ) ∧ VISITS ( x , y ))) There is one representative for all customers. ∃ x ( REPRESENTATIVE ( x ) ∧ ∀ y ( CUSTOMER ( y ) → VISITS ( x , y ))) Given that we only have one syntactic structure, how can we represent the ambiguity? Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 5 / 44
Quantifier Storage to the Rescue! “Cooper Storage” As a sentence is parsed, quantifiers go into storage as they are encountered They can be retrieved appropriately when enough information Goal: Represent all possibilities Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 6 / 44
� � Quantifier Scope Ambiguity A unicorn appears to be approaching. A unicorn appears to be approaching . exists ( 1 ) may not exist ( 2 ) Something appears to be approaching, and it is a unicorn. 1 Something appears to be approaching, and it appears to be a 2 unicorn. Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 7 / 44
Development of Quantification in HPSG Pollard and Sag (1994) (from Pollard and Yoo (1998)) 2 3 sign � every student � 6 PHONOLOGY 7 6 7 6 7 2 3 " # 6 CATEGORY | HEAD noun 7 6 7 LOCAL 6 7 6 npro 7 CONTENT SYNSEM 6 7 1 = [ ∀ y | student ( y )] 6 7 6 7 4 5 6 7 nonlocal NONLOCAL 6 7 6 7 6 7 n o 6 7 1 QSTORE 6 7 4 5 �� RETRIEVED Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 8 / 44
Development of Quantification in HPSG Pollard and Yoo (1998) 2 sign 3 list(phonstring) PHONOLOGY 6 7 6 7 6 7 2 3 2 3 category 6 CATEGORY 7 6 7 6 content 7 6 7 6 CONTENT 7 6 6 7 7 LOCAL 6 7 SYNSEM 6 6 7 7 set(quantifier) 6 7 QSTORE 6 6 7 7 4 5 6 4 5 7 set(quantifier) 6 POOL 7 6 7 4 5 list(quantifier) RETRIEVED Fixed: Filler-gap and raising constructions Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 9 / 44
Agenda Background 1 Przepiórkowski 1998 2 Development of the Grammar 3 In Action 4 Summary 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 10 / 44
Fixes Simpler analysis: completely lexical No complex constraints Semantics completely in CONTENT Works with traceless extractions [ ARG - ST ] PY: Retrieval at all psoa s → spurious ambiguities [word restriction] Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 11 / 44
Spurious Ambiguities in PY Retrievals at VP 2 , VP 3 , VP 4 , and V 4 yield the same reading Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 12 / 44 Figure:
Overview 2 3 word 2 3 content . . . 6 7 (1.2a) (1.2b) 6 7 n o 4 5 quant * n o QSTORE 4 5 NEW - QUANTIFIERS quant * � ������� � � � � � � psoa nom-obj quant (1.3) word → Desc 1 ∨ Desc 2 2 3 2 3 psoa " # nom-obj ∨ quant 6 7 6 7 SS | LOC | CONT ∨ QSTORE 2 6 7 6 7 (1.4) Desc 1 = 1 6 QSTORE 7 4 5 6 7 QUANTS 3 6 7 4 5 NEW - QUANTIFIERS 5 where 1 = 5 ⊎ union QSTORE s of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4 2 3 SS | LOC | CONT 1 (1.5) Desc 2 = fi fl 6 7 h i . . . , SS | LOC | CONT 1 , . . . ARG - ST 4 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44
Overview 2 3 word 2 3 content . . . 6 7 (1.2a) (1.2b) 6 7 n o 4 5 quant * n o QSTORE 4 5 NEW - QUANTIFIERS quant * � ������� � � � � � � psoa nom-obj quant (1.3) word → Desc 1 ∨ Desc 2 2 3 2 3 psoa " # nom-obj ∨ quant 6 7 6 7 SS | LOC | CONT ∨ QSTORE 2 6 7 6 7 (1.4) Desc 1 = 1 6 QSTORE 7 4 5 6 7 QUANTS 3 6 7 4 5 NEW - QUANTIFIERS 5 where 1 = 5 ⊎ union QSTORE s of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4 2 3 SS | LOC | CONT 1 (1.5) Desc 2 = fi fl 6 7 h i . . . , SS | LOC | CONT 1 , . . . ARG - ST 4 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44
Overview 2 3 word 2 3 content . . . 6 7 (1.2a) (1.2b) 6 7 n o 4 5 quant * n o QSTORE 4 5 NEW - QUANTIFIERS quant * � ������� � � � � � � psoa nom-obj quant (1.3) word → Desc 1 ∨ Desc 2 2 3 2 3 psoa " # nom-obj ∨ quant 6 7 6 7 SS | LOC | CONT ∨ QSTORE 2 6 7 6 7 (1.4) Desc 1 = 1 6 QSTORE 7 4 5 6 7 QUANTS 3 6 7 4 5 NEW - QUANTIFIERS 5 where 1 = 5 ⊎ union QSTORE s of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4 2 3 SS | LOC | CONT 1 (1.5) Desc 2 = fi fl 6 7 h i . . . , SS | LOC | CONT 1 , . . . ARG - ST 4 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44
Overview 2 3 word 2 3 content . . . 6 7 (1.2a) (1.2b) 6 7 n o 4 5 quant * n o QSTORE 4 5 NEW - QUANTIFIERS quant * � ������� � � � � � � psoa nom-obj quant (1.3) word → Desc 1 ∨ Desc 2 2 3 2 3 psoa " # nom-obj ∨ quant 6 7 6 7 SS | LOC | CONT ∨ QSTORE 2 6 7 6 7 (1.4) Desc 1 = 1 6 QSTORE 7 4 5 6 7 QUANTS 3 6 7 4 5 NEW - QUANTIFIERS 5 where 1 = 5 ⊎ union QSTORE s of selected arguments 4 = set of elements of 3 1 = 2 ⊎ 4 2 3 SS | LOC | CONT 1 (1.5) Desc 2 = fi fl 6 7 h i . . . , SS | LOC | CONT 1 , . . . ARG - ST 4 5 Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 13 / 44
Concepts QSTORE filled from selected arguments QSTORE accumulates quantifiers from QSTORE s of those members of ARG - ST not raised from other arguments ARGUMENT - STRUCTURE Semantics-driven subcategorization frame Devolution of Semantics Principle “The CONTENT value of a phrase is token-identical to that of the head daughter.” (PS94) Jonathan Khoo (jkhoo@sfs) Quantification & TRALE Grammar Engineering SS06 14 / 44
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