DOCSLIB.ORG

Logical Dependency in Quantification: a Study Conducted Within The

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

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 ...............................................................................
Recommended publications
  • Reasoning About Knowledge in Philosophy; the Paradigm of Epistemic Logic

    Reasoning About Knowledge in Philosophy; the Paradigm of Epistemic Logic

    REASONING ABOUT KNOWLEDGE IN PHILOSOPHY; THE PARADIGM OF EPISTEMIC LOGIC Jaakko Hintikka Department of Philosophy Florida State University Tallahassee, FL 32306 ABSTRACT Theories of knowledge representation and reasoning about knowledge in philosophy are considered from the vantage point of epistemic logic. This logic is primarily a logic of knowing that, and its semantics can be considered an explication of the well-known idea that "information means elimination of uncertainty". A number of other theories are discussed as further developments of epistemic logic. They include: (1) theory of questions and answers. (2) interplay of quantifiers and epistemic concepts. (3) representations of other kinds of knowledge than knowing that, especially those expressed by knows + an indirect wh-question and by knows + direct grammatical object: (4) the problem of cross-identification; the coexistence of different cross-identification methods. (5) the problem of logical omniscience. {6) informational independence in epistemic logic and its manifestations, including the de dicto - de re contrast and wh-questions with outside quantifiers. (7) an interrogative model of inquiry and its applications, especially the conceptualization of tacit knowledge and of range of attention. 63 64 SESSION2 Epistemic logic as a vehicle of knowledge representation The main vehicle of speaking a~d reasoning about knowledge in philosophy has recently been epistemic logic° Even though epistemic logic is not the only relevant language-game in town, it offers a useful perspective here, for certain other approaches can be thought of as improvements on epistemic logic. In its axiomatic-deductive forms, epistetnic logic is normally considered a branch of modal logic, and its semantics is usually subsumed under the misleading heading of "possible-worlds semantics".
  • Quantifiers Vs. Quantification Theory

    Quantifiers Vs. Quantification Theory

    Quantifiers vs. Quantification Theory by JAAKKO HINTIKKA The syntax and semantics of quantifiers is of crucial significance in current linguistic theorizing for more than one reason. The last statement of his grammatical theories by the late Richard Montague (1973) is modestly entitled “The Proper Treatment of Quantification in Ordinary English”. In the authoritative statement of his “Generative Semantics”, George Lakoff (1971, especially pp. 238-267) uses as his first and foremost testing-ground the grammar of certain English quantifiers. In particular, they serve to illustrate, and show need of, his use of global constraints governing the derivation of English sen- tences. Evidence from the behavior of quantifiers (including numerical expressions 1) has likewise played a major role in recent discussions of such vital problems as the alleged meaningdpreservation of transfor- mations, 2 co-reference, 3 the role of surface structure in semantical interpretation, and so on. In all these problems, the behavior of natural-language quantifiers is one of the main issues. Quantifiers have nevertheless entered the Methodenstreit of contemporary linguistics in another major way, too. (These two groups of problems are of course interrelated.) This is the idea that the structures studied iln the so-called quantification theory of symbolic logic-otherwise know as first-order logic, (lower) predicate calculus, or elementary logic-can serve and suffice 6 as semantical representations of English sentences. Views of this general type have been proposed by McCawley (1971)* and Lakoff (1972)’ (among others). A related theory of “Deep Structure as Logical Form” has been put forward and defended by G. Harman (1972).
  • Dialetheism, Game Theoretic Semantics, and Paraconsistent

    Dialetheism, Game Theoretic Semantics, and Paraconsistent

    Dialetheism, Game Theoretic Semantics, and Paraconsistent Team Semantics Pietro Galliani Abstract. We introduce a variant of Dependence Logic in which truth is defined not in terms of existence of winning strategies for the Proponent (Eloise) in a semantic game, but in terms of lack of winning strategies for the Opponent (Abelard). We show that this language is a conserva- tive but paraconsistent extension of First Order Logic, that its validity problem can be reduced to that of First Order Logic, that it capable of expressing its own truth and validity predicates, and that it is expres- 1 sively equivalent to Universal Second Order Logic Π1. Furthermore, we prove that a Paraconsistent Non-dependence Logic formula is consistent if and only if it is equivalent to some First Order Logic sentence; and we show that, on the other hand, all Paraconsistent Dependence Logic sentences are equivalent to some First Order sentence with respect to truth (but not necessarily with respect to falsity). Mathematics Subject Classification (2010). Primary 03B53 ; Secondary 03B60. Keywords. Paraconsistency, Team Semantics, Game Theoretic Seman- tics. arXiv:1206.6573v2 [math.LO] 14 Mar 2014 1. Introduction Dialetheism is the philosophical position according to which there exist true contradictions. It has been proposed as a possible answer to the paradoxes of self-reference; and moreover, although this is of less relevance for the purposes of this work, it also is one potential approach to the logical treatment of vagueness and transition states.1 Even though dialetheism is not the only possible motivation for the study of paraconsistent logics, that is, logics in which the principle of explo- sion (“Ex contradictione quodlibet”: from a contradiction, everything can be The author acknowledges the support of the Deutsche Forschungsgemeinschaft (project number DI 561/6-1).
  • The Epistemic Logic of IF Games

    The Epistemic Logic of IF Games

    1 The epistemic logic of IF games Johan van Benthem, Amsterdam & Stanford December 2002 To appear in the Hintikka Volume, Library of Living Philosophers. Abstract We analyze IF/hyper-classical games by bringing together two viewpoints from Jaakko Hintikka's work: game semantics, and epistemic logic. In the process, we link up between logic and game theory. 1 Logic meets games Game theory and logic met in the 1950s – and Jaakko Hintikka has been a pioneer ever since in introducing game-theoretic viewpoints into logic, from his early basic evaluation games for predicate logic to his more recent ‘information-friendly’ logic based on extended games that go far beyond classical systems. The grand philosophical program behind these technical efforts is found in his books “Logic, Language Games and Information” (1973), “The Game of Language” (1985), the Handbook of Logic & Language chapter with Gabriel Sandu on ‘Game-Theoretical Semantics’ (1997), and many recent papers and manifestoes (cf. Hintikka 2002). Connections between logic and games are attracting attention these days, ranging from special-purpose ‘logic games’ to 'game logics' analyzing general game structure (cf. the general program in van Benthem 1999–2002). IF logic is intriguing in this respect, as it sits at the interface of ordinary logic games, whose players have perfect information about their position during play, and general game theory, where players may typically have imperfect information of various sorts. My aim in this paper is to explore the game content of Hintikka’s systems using tools from epistemic logic, and more generally, clarify their thrust at the interface of logic and game theory.
  • Logic A-Z from Wikipedia, the Free Encyclopedia Chapter 1

    Logic A-Z from Wikipedia, the Free Encyclopedia Chapter 1

    Logic A-Z From Wikipedia, the free encyclopedia Chapter 1 Antepredicament Antepredicaments, in logic, are certain previous matters requisite to a more easy and clear apprehension of the doctrine of predicaments or categories. Such are definitions of common terms, as equivocals, univocals, etc., with divisions of things, their differences, etc. They are thus called because Aristotle treated them before the predicaments, hoping that the thread of discourse might not afterwards be interrupted. 1.1 References • This article incorporates text from a publication now in the public domain: Chambers, Ephraim, ed. (1728). "*article name needed". Cyclopædia, or an Universal Dictionary of Arts and Sciences (first ed.). James and John Knapton, et al. 2 Chapter 2 Apophasis Not to be confused with Apophysis (disambiguation), Apoptosis, or Apophis (disambiguation). Apophasis is a rhetorical device wherein the speaker or writer brings up a subject by either denying it, or denying that it should be brought up.*[1] Accordingly, it can be seen as a rhetorical relative of irony. Also called paralipsis (παράλειψις) – also spelled paraleipsis or paralepsis –, or occupatio,*[2]*[3]*[4]*[5] and known also as prae- teritio, preterition, antiphrasis (ἀντίφρασις), or parasiopesis (παρασιώπησις), apophasis is usually employed to make a subversive ad hominem attack, which makes it a frequently used tactic in political speeches to make an attack on one's opponent. Using apophasis in this way is often considered to be bad form. The device is typically used to distance
  • A Compositional Game Semantics for Multi-Agent Logics of Partial Information

    A Compositional Game Semantics for Multi-Agent Logics of Partial Information

    A Compositional Game Semantics for Multi-Agent Logics of Partial Information Samson Abramsky Oxford University Computing Laboratory Abstract We consider the following questions: What kind of logic has a natural semantics in multi-player (rather than 2-player) games? How can we express branching quantifiers, and other partial-information constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on Kahn-Plotkin concrete domains. Partial information constraints are represented as co-closure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and co-arities. This enables a fully compositional account of a wide range of features in a multi-agent, concurrent setting, including IF-style quantifiers. Contents 1 Introduction 2 2 From 2-person to n-person games 3 2.1 Thenaturalnessof2-persongames . ..... 3 2.2 Background: 2-persongames . ... 3 2.3 AnAside ...................................... 4 2.4 From 2-person to n-persongames......................... 4 3 Semantics of LA 5 3.1 Static Semantics: Concrete Data Structures as Concurrent Games . 6 3.2 Dynamic Semantics: Concurrent Strategies . ........ 10 3.2.1 Inductive Construction of Strategy Sets . ...... 10 3.2.2 Local conditions on strategies . 11 3.2.3 Global definitions of strategy sets . ..... 12 3.2.4 Comparison of the local and global definitions . ....... 14 3.3 Evaluation of Strategy Profiles . ..... 16 3.4 OutcomesandValuations . 17 4 Towards environmentally friendly logic 19 4.1 SyntaxasaCategory............................... 19 4.2 Static Semantics Revisited . ..... 20 4.3 Interlude: StructuralCongruence .