LOGICAL DEPENDENCY IN QUANTIFICATION — A Study Conducted within the Framework of Labelled Deductive Systems, with Special Reference to English and Mandarin Chinese Yan Jiang A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Ph.D. University College, London 1995 ProQuest Number: 10045810 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest. ProQuest 10045810 Published by ProQuest LLC(2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code. Microform Edition © ProQuest LLC. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 " Logicians should note that a deductive system is concerned not Just with un labelled entaiiments or sequents A-* B (as in Gentzen’s proof theory), but with deductions or proofs of such entaiiments. in writing f: A ^B we think offas the 'reason’ why A entails B." (Lambek & Scott 1986) " Once we have introduced the notion of a ’considered’ choice to eliminate quantifiers, we may wonder whether we cannot describe a quantifier exhaustively in terms of assignment statements with the appropriate argument That is, can a quantifier be proof-theoreticaiiy described purely in terms of the assignments that are used to eliminate and introduce it ?" (Meyer Viol 1995) "...while aiming at finding out how Chinese logic operates, we shall probably end up with finding out how logic operates in Chinese. " (Yuen Ren Chao 1976) Acknowledgements My greatest thanks go to Ruth Kempson and Deirdre Wilson. Ruth has been my mentor over the past five years. It was mainly from Ruth that I acquired knowledge of formal semantics and logic. To be constantly inspired by Ruth’s new ideas, to be urged by Ruth to take in new views and techniques in logic and formal semantics, to worry over the LDS solutions together with Ruth..., these formed the most exciting part of my study which I will treasure for the rest of my life. I thank Ruth for her unfailing support, for her encouragement over every progress I made, for her generosity in spending hours of hours of her time discussing with me issues in syntax, semantics and logic, and for her many helpful suggestions and comments which greatly improved the quality of this thesis. Equally indebted am I to Deirdre for teaching me relevance theory, semantics and philosophy of language, for her support to my commitment to the study of LDS which takes relevance theory as a major theoretical underpinning, and for her insightful comments on my manuscripts. Ruth and Deirdre would never hesitate in pointing out my misinterpretations, erroneous conclusions, and sheer stupidity which surfaced all too frequently. Needless to say, whatever errors that still remain in this thesis are all mine. Besides, I owe a special debt to Ruth and Deirdre for their understanding and help in matters other than linguistics. I can never thank them well enough. I also want to thank the other teachers in the departments of linguistics at UCL 4 and SOAS for their teaching, help, and friendship: David Bennett, Misi Brody, Robyn Carston, Wynn Chao, Monik Charette, Billy Clark, Dick Hudson, Johnathan Kaye, Hans van de Koot, Michael Man, Rita Manzini and Neil Smith. Thanks to Wynn Chao, Marjolein Groefsema, Ruth Kempson and Villy Rochota, for whom I worked respectively as teaching assistant. Besides UCL and SOAS, I owe a lot to two people at Imperial College: to Dov Gabbay, whose LDS provides the logical framework within which I conducted my research work, and whose talks at the LORE seminar between 1991 and 1992 helped me to come to grips with LDS; to Ruy de Queiroz, whose discussion with me about E-calculus, Arbitrary Objects and LDS helped disentangle many puzzling issues. Thanks to the organizers and members of Ruth Kempson’s LDS Seminar (SOAS), Wynn Chao’s Syntax Workshop(SOAS), the 1990-1991 Chinese Syntax Seminar(SOAS), the UCL Postgraduate Seminar, the UCL Relevance Discussion Group, Misi Brody’s Syntax Reading Group(UCL), and the LORE Seminar(lmperial College), at some sessions of which(except for the last one) 1 gave presentations and from all of which 1 benefitted greatly. Thanks to the SBFSS for supporting my study in UK from 1989 to 1993 and for funding my attendance of the 4th ESSLLI Summer School in Essex. Back to the years before 1 went to study in Britain. At Fudan University, 5 Shanghai, Liejiong Xu was my BA and MA theses supervisor. I thank him for innitiating me into the realm of linguistics and for sharing with me the excitement of doing syntax. I am also grateful to Yiimin Cheng for acquainting me with issues in pragmatics, stylistics, and structuralist linguistics and to San Duanmu for his teaching in phonetics and phonology. f I thank linguists and philosophers visiting Fudan for broadening my mind, for commenting on my papers, for sending me their works, and for giving me constant encouragements, especially: Jerrold Katz, Guido Kiing, James McCawley, and Fritz Newmeyer. Since late 1993,1 have been working at the Department of Chinese & Bilingual Studies, Hong Kong Polytechnic University. I am especially grateful to Yat-sing Cheung, then head of the department and now deputy dean of Faculty of Communication, and Kwan-hin Cheung, now head of the department, for their trust, encouragement, consideration and support. Thanks to my colleagues both at Polytechnic University and at other universities in Hong Kong for friendship and for discussions on issues related to this thesis and to linguistics at large: Yang Gu, Yuanjian He, Thomas Hun-tak Lee, Daniel Yuanliang Ngai, Haihua Pan, Tim Dingxu Shi, Zhixiang Tang, Jenny Zhijie Wang, Doreen Dongying Wu, Liejiong Xu, Yulong Xu, and Xiaoheng Zhang. I also thank Department of CBS of Polytechnic University for generously supporting my attendance of ICCL-3 in Hong Kong and the 7th ESSLLI Summer School in Barcelona. 6 Finally, thanks to my parents for their support, and to my wife. May, for her love and understanding, and for her willingness in wading through with me all the turbulent waves in life. Abstract This thesis is a study on quantification in the formal logical system of Labelled Deductive Systems as applied to Natural Language Understanding (LDS^l for short). Chapter 1 starts with a discussion on the treatment of quantification in the GB framework, followed by an examination on branching quantification. Then, in Chapter 2, details of LDS^^ are introduced in a way that its logical motivations are explained in the context of natural language understanding. Chapter 3 first discusses Game- theoretic Semantics and its treatment of quantifiers. This is followed by discussions of some other procedural treatments of quantification alternative to the first-order treatments. After that, detailed treatments of quantification in English by LDS^l proposed by Gabbay & Kempson (1992b) are presented in Chapter 4. Instead of viewing quantifiers as operators, I have followed the works of Gabbay & Kempson in treating them as words projecting meta-variables over the labels, whose values are to be instantiated in the dynamic process of utterance interpretation, which is conceived as a procedural, proof-deductive process. Instantiation of variables will bring about the construction of dependency relation, the varieties of which lead to ambiguity of scope. Chapter 5 first presents the crucial data in Chinese and a short survey of the past literature. It then gives an analysis of Chinese quantification in LDS^l as well as a comparative study of the phenomenon between Chinese and English. Different properties of quantification between English and Chinese are attributed to a delaying mechanism which is at work in English but not in Chinese. A deeper linguistic 8 motivation is given in the form of the Kempson & Jiang Hypothesis. Additional supporting evidence for the hypothesis is also provided from the study of double­ object constructions and dative/locative constructions. A comparative discussion between LDS^l and treatments in Categorial Grammars and Discourse Representation Theory is given in Chapter 6. The thesis also attempts to relate the notions, mechanisms and findings in LDS to other linguistic frameworks, notably the Government-Binding Theory, Montague Semantics, Categorial Grammars, Discourse Representation Theory, Game-Theoretical Semantics and Branching Quantifier Theory. CONTENTS Acknowledgements .................................................................................................... 3 Abstract .......................................................................................................................... 7 Chapter 1. Quantifiers and Quantification Theory .................................................... 14 0. Preamble ........................................................................................................... 14 1. Q R atL F ......................................................................................................... 15 2. The Branching Quantifier A naly sis .............................................................. 22 2.1. Linear and Branching Quantification ............................................................ 22 2.2. BQ in Natural Language ...............................................................................