Homogeneity in Donkey Sentences
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Natural Language Semantics
Logical Approaches to (Compositional) Natural Language Semantics Kristina Liefke, MCMP Summer School on Mathematical Philosophy for Female Students LMU Munich, July 28, 2014 This Session & The Summer School Many lectures/tutorials have presupposed the possibility of translating natural language sentences into interpretable logical formulas. But: This translation procedure has not been made explicit. 1 In this session, we introduce a procedure for the translation of natural language, which is inspired by the work of Montague: Kristina talks about Montague. Kristina k Montague m talk talk about about Kristina talks about Montague about (m, talk, k) 2 We will then use this procedure to provide a (formal) semantics for natural language. Montague Grammar The (Rough) Plan nat. lang. logical model-th. sentences formulas objects translation interpret’n K. talks talk (k) T À Compositional Semantics We will be concerned with compositional – not lexical – semantics: Lexical semantics studies the meaning of individual words: talk := “to convey or express ideas, thought, information etc. by means of speech” J K Compositional semantics studies the way in which complex phrases obtain a meaning from their constituents: Kristina = k Montague = m talk = talk about = about Kristina talks about Montague = about (m, talk, k) J K J K J K J K J K J K J K J K PrincipleJ (Semantic compositionality)K J K (Partee, 1984) The meaning of an expression is a function of the meanings of its constituents and their mode of combination. Compositional Semantics We will be concerned with compositional – not lexical – semantics: Lexical semantics studies the meaning of individual words. Compositional semantics studies the way in which complex phrases obtain a meaning from their constituents: Montague: Kristina = k0 Montague = m0 talk = talk0 about = about0 Kristina talks about Montague = about0(m0, talk0, k0) J K J K J K J K J K J K J K J K J ‘Word-prime semantics’ (CrouchK J and King, 2008),K cf. -
Anaphoric Reference to Propositions
ANAPHORIC REFERENCE TO PROPOSITIONS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Todd Nathaniel Snider December 2017 c 2017 Todd Nathaniel Snider ALL RIGHTS RESERVED ANAPHORIC REFERENCE TO PROPOSITIONS Todd Nathaniel Snider, Ph.D. Cornell University 2017 Just as pronouns like she and he make anaphoric reference to individuals, English words like that and so can be used to refer anaphorically to a proposition introduced in a discourse: That’s true; She told me so. Much has been written about individual anaphora, but less attention has been paid to propositional anaphora. This dissertation is a com- prehensive examination of propositional anaphora, which I argue behaves like anaphora in other domains, is conditioned by semantic factors, and is not conditioned by purely syntactic factors nor by the at-issue status of a proposition. I begin by introducing the concepts of anaphora and propositions, and then I discuss the various words of English which can have this function: this, that, it, which, so, as, and the null complement anaphor. I then compare anaphora to propositions with anaphora in other domains, including individual, temporal, and modal anaphora. I show that the same features which are characteristic of these other domains are exhibited by proposi- tional anaphora as well. I then present data on a wide variety of syntactic constructions—including sub- clausal, monoclausal, multiclausal, and multisentential constructions—noting which li- cense anaphoric reference to propositions. On the basis of this expanded empirical do- main, I argue that anaphoric reference to a proposition is licensed not by any syntactic category or movement but rather by the operators which take propositions as arguments. -
A Guide to Dynamic Semantics
A Guide to Dynamic Semantics Paul Dekker ILLC/Department of Philosophy University of Amsterdam September 15, 2008 1 Introduction In this article we give an introduction to the idea and workings of dynamic se- mantics. We start with an overview of its historical background and motivation in this introductory section. An in-depth description of a paradigm version of dynamic semantics, Dynamic Predicate Logic, is given in section 2. In section 3 we discuss some applications of the dynamic kind of interpretation to illustrate how it can be taken to neatly account for a vast number of empirical phenom- ena. In section 4 more radical extensions of the basic paradigm are discussed, all of them systematically incorporating previously deemed pragmatic aspects of meaning in the interpretational system. Finally, a discussion of some more general, philosophical and theoretical, issues surrounding dynamic semantics can be found in section 5. 1.1 Theoretical Background What is dynamic semantics. Some people claim it embodies a radical new view of meaning, departing from the main logical paradigm as it has been prominent in most of the previous century. Meaning, or so it is said, is not some object, or some Platonic entity, but it is something that changes information states. A very simple-minded way of putting the idea is that people uses languages, they have cognitive states, and what language does is change these states. “Natu- ral languages are programming languages for minds”, it has been said. Others build on the assumption that natural language and its interpretation is not just concerned with describing an independently given world, but that there are lots of others things relevant in the interpretation of discourse, and lots of other functions of language than a merely descriptive one. -
Introduction to Montague Semantics Studies in Linguistics and Philosophy
INTRODUCTION TO MONTAGUE SEMANTICS STUDIES IN LINGUISTICS AND PHILOSOPHY formerly Synthese Language Library Managing Editors: GENNORO CHIERCHIA, Cornwell University PAULINE JACOBSON, Brown University Editorial Board: EMMON BACH, University of Massachusetts at Amherst JON BARWISE, CSLI, Stanford JOHAN VAN BENTHEM, Mathematics Institute, University of Amsterdam DAVID DOWTY, Ohio State University, Columbus GERALD GAZDAR, University of Sussex, Brighton EWAN KLEIN, University of Edinburgh BILL LADUSA W, University of California at Santa Cruz SCOTT SOAMES, Princeton University HENRY THOMPSON, University of Edinburgh VOLUM E 11 INTRODUCTION TO MONTAGUE SEMANTICS by DA VID R. DOWTY Dept. of Linguistics, Ohio State University, Columbus ROBERT E. WALL Dept. of Linguistics, University of Texas at Austin and STANLEY PETERS CSLI, Stanford KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON library of Congress Cataloging in Publication Data Dowty, David R. Introduction to Montague semantics. (Syn these language library; v. 11) Bibliography: p. Includes index. 1. Montague grammar. 2. Semantics(philosophy). 3. Generative grammar. 4. Formal languages-Semantics. I. Wall, Robert Eugene, joint author. II. Peters, Stanley, 1941- joint author. III. Title. IV. Series P158.5D6 415 80-20267 ISBN-13: 978-90-277-1142-7 e-ISBN-13978-94-009-9065-4 DOl: 10.1007/978-94-009-9065-4 Published by Kluwer Academic Publishers, P.O. Box 17,3300 AA Dordrecht, The Netherlands. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. -
Chapter 3 Describing Syntax and Semantics
Chapter 3 Describing Syntax and Semantics 3.1 Introduction 110 3.2 The General Problem of Describing Syntax 111 3.3 Formal Methods of Describing Syntax 113 3.4 Attribute Grammars 128 3.5 Describing the Meanings of Programs: Dynamic Semantics 134 Summary • Bibliographic Notes • Review Questions • Problem Set 155 CMPS401 Class Notes (Chap03) Page 1 / 25 Dr. Kuo-pao Yang Chapter 3 Describing Syntax and Semantics 3.1 Introduction 110 Syntax – the form of the expressions, statements, and program units Semantics - the meaning of the expressions, statements, and program units. Ex: the syntax of a Java while statement is while (boolean_expr) statement – The semantics of this statement form is that when the current value of the Boolean expression is true, the embedded statement is executed. – The form of a statement should strongly suggest what the statement is meant to accomplish. 3.2 The General Problem of Describing Syntax 111 A sentence or “statement” is a string of characters over some alphabet. The syntax rules of a language specify which strings of characters from the language’s alphabet are in the language. A language is a set of sentences. A lexeme is the lowest level syntactic unit of a language. It includes identifiers, literals, operators, and special word (e.g. *, sum, begin). A program is strings of lexemes. A token is a category of lexemes (e.g., identifier). An identifier is a token that have lexemes, or instances, such as sum and total. Ex: index = 2 * count + 17; Lexemes Tokens index identifier = equal_sign 2 int_literal * mult_op count identifier + plus_op 17 int_literal ; semicolon CMPS401 Class Notes (Chap03) Page 2 / 25 Dr. -
Situations and Individuals
Forthcoming with MIT Press Current Studies in Linguistics Summer 2005 Situations and Individuals Paul Elbourne To my father To the memory of my mother Preface This book deals with the semantics of the natural language expressions that have been taken to refer to individuals: pronouns, definite descriptions and proper names. It claims, contrary to previous theorizing, that they have a common syntax and semantics, roughly that which is currently associated by philosophers and linguists with definite descriptions as construed in the tradition of Frege. As well as advancing this proposal, I hope to achieve at least one other aim, that of urging linguists and philosophers dealing with pronoun interpretation, in particular donkey anaphora, to consider a wider range of theories at all times than is sometimes done at present. I am thinking particularly of the gulf that seems to have emerged between those who practice some version of dynamic semantics (including DRT) and those who eschew this approach and claim that the semantics of donkey pronouns crucially involves definite descriptions (if they consider donkey anaphora at all). In my opinion there is too little work directly comparing the claims of these two schools (for that is what they amount to) and testing them against the data in the way that any two rival theories might be tested. (Irene Heim’s 1990 article in Linguistics and Philosophy does this, and largely inspired my own project, but I know of no other attempts.) I have tried to remedy that in this book. I ultimately come down on the side of definite descriptions and against dynamic semantics; but that preference is really of secondary importance beside the attempt at a systematic comparative project. -
Montague Grammar Stefan Thater Blockseminar “Underspecification” 10.04.2006 Overview
Montague Grammar Stefan Thater Blockseminar “Underspecification” 10.04.2006 Overview • Introduction • Type Theory • A Montague-Style Grammar • Scope Ambiguities • Summary Introduction • The basic assumption underlying Montague Grammar is that the meaning of a sentence is given by its truth conditions. - “Peter reads a book” is true iff Peter reads a book • Truth conditions can be represented by logical formulae - “Peter reads a book” → ∃x(book(x) ∧ read(p*, x)) • Indirect interpretation: - natural language → logic → models Compositionality • An important principle underlying Montague Grammar is the so called “principle of compositionality” The meaning of a complex expression is a function of the meanings of its parts, and the syntactic rules by which they are combined (Partee & al, 1993) Compositionality John reads a book John reads a book [[ John reads a book ]] = reads a book C1([[ John]], [[reads a book]] ) = C1([[ John]], C2([[reads]] , [[a book]] ) = a book C1([[ John]], C2([[reads]] , C3([[a]], [[book]])) Representing Meaning • First order logic is in general not an adequate formalism to model the meaning of natural language expressions. • Expressiveness - “John is an intelligent student” ⇒ intelligent(j*) ∧ stud(j*) - “John is a good student” ⇒ good(j*) ∧ stud(j*) ?? - “John is a former student” ⇒ former(j*) ∧ stud(j*) ??? • Representations of noun phrases, verb phrases, … - “is intelligent” ⇒ intelligent( ∙ ) ? - “every student” ⇒ ∀x(student(x) ⇒ ⋅ ) ??? Type Theory • First order logic provides only n-ary first order relations, which -
A Dynamic Semantics of Single-Wh and Multiple-Wh Questions*
Proceedings of SALT 30: 376–395, 2020 A dynamic semantics of single-wh and multiple-wh questions* Jakub Dotlacilˇ Floris Roelofsen Utrecht University University of Amsterdam Abstract We develop a uniform analysis of single-wh and multiple-wh questions couched in dynamic inquisitive semantics. The analysis captures the effects of number marking on which-phrases, and derives both mention-some and mention-all readings as well as an often neglected partial mention- some reading in multiple-wh questions. Keywords: question semantics, multiple-wh questions, mention-some, dynamic inquisitive semantics. 1 Introduction The goal of this paper is to develop an analysis of single-wh and multiple-wh questions in English satisfying the following desiderata: a) Uniformity. The interpretation of single-wh and multiple-wh questions is derived uniformly. The same mechanisms are operative in both types of questions. b) Mention-some vs mention-all. Mention-some and mention-all readings are derived in a principled way, including ‘partial mention-some readings’ in multiple-wh questions (mention-all w.r.t. one of the wh-phrases but mention-some w.r.t. the other wh-phrase). c) Number marking. The effects of number marking on wh-phrases are captured. In particular, singular which-phrases induce a uniqueness requirement in single-wh questions but do not block pair-list readings in multiple-wh questions. To our knowledge, no existing account fully satisfies these desiderata. While we cannot do justice to the rich literature on the topic, let us briefly mention a number of prominent proposals. Groenendijk & Stokhof(1984) provide a uniform account of single-wh and multiple-wh ques- tions, but their proposal does not successfully capture mention-some readings and the effects of number marking. -
Free Choice and Homogeneity
Semantics & Pragmatics Volume 12, Article 23, 2019 https://doi.org/10.3765/sp.12.23 This is an early access version of Goldstein, Simon. 2019. Free choice and homogeneity. Semantics and Prag- matics 12(23). 1–47. https://doi.org/10.3765/sp.12.23. This version will be replaced with the final typeset version in due course. Note that page numbers will change, so cite with caution. ©2019 Simon Goldstein This is an open-access article distributed under the terms of a Creative Commons Attribution License (https://creativecommons.org/licenses/by/3.0/). early access Free choice and homogeneity* Simon Goldstein Australian Catholic University Abstract This paper develops a semantic solution to the puzzle of Free Choice permission. The paper begins with a battery of impossibility results showing that Free Choice is in tension with a variety of classical principles, including Disjunction Introduction and the Law of Excluded Middle. Most interestingly, Free Choice appears incompatible with a principle concerning the behavior of Free Choice under negation, Double Prohibition, which says that Mary can’t have soup or salad implies Mary can’t have soup and Mary can’t have salad. Alonso-Ovalle 2006 and others have appealed to Double Prohibition to motivate pragmatic accounts of Free Choice. Aher 2012, Aloni 2018, and others have developed semantic accounts of Free Choice that also explain Double Prohibition. This paper offers a new semantic analysis of Free Choice designed to handle the full range of impossibility results involved in Free Choice. The paper develops the hypothesis that Free Choice is a homogeneity effect. -
Meanings of Determiners Heading Non-Topic Dps to the Meanings of the Corresponding Topics
Acknowledgements First of all, I would like to thank my teachers and supervisors Manfred Bierwisch and Reinhard Blutner. Without their sympathetic help in a personally very difficult situation, I would have been unable even to start writing this dissertation. Besides this, they patiently supported me with their advice and experience in every stage of my work. The people that inspired me with discussions and comments are so numerous that there is no hope to mention all of them. Among them are Kai Alter, Daniel Büring, Johannes Dölling, Bernhard Drubig, Hans Martin Gärtner, Edward Göbbel, Michael Herweg, Caroline Heycock, Helen de Hoop, Inga Kohlhof, Manfred Krifka, Annette Lessmöllmann, Christine Maaßen, André Meinunger, Marga Reis, Michal Starke, Markus Steinbach, Wolfgang Sternefeld, Anatoli Strigin, Hubert Truckenbrodt, Enric Vallduví, Ralf Vogel, Chris Wilder, Susanne Winkler, Werner Wolff, Henk Zeevat, and Ede Zimmermann. I am indebted to the "Max-Planck-Gesellschaft" for its financial support. Special thanks go to Elena Demke, Annette Lessmöllmann, Anatoli Strigin, and Chris Wilder for correcting my English. All remaining mistakes are of course subject to my own responsibility. Last but not least, I thank my parents and my brother for everything. Table of Contents 1 Introduction . 1 2 The Dynamic Framework . 5 2.1 Donkey Sentences and Cross-sentential Anaphora . 5 2.2 Montague Semantics and File Change Semantics: A Comparison . 7 2.2.1 Montague Semantics: The General Picture . 7 2.2.2 File Change Semantics: An Overview . 11 2.2.2.1 The Strategy . 11 2.2.2.2 Files . 13 2.2.2.3 LF-Construal . 13 2.2.2.4 The Interpretation of LF . -
Chapter 3 – Describing Syntax and Semantics CS-4337 Organization of Programming Languages
!" # Chapter 3 – Describing Syntax and Semantics CS-4337 Organization of Programming Languages Dr. Chris Irwin Davis Email: [email protected] Phone: (972) 883-3574 Office: ECSS 4.705 Chapter 3 Topics • Introduction • The General Problem of Describing Syntax • Formal Methods of Describing Syntax • Attribute Grammars • Describing the Meanings of Programs: Dynamic Semantics 1-2 Introduction •Syntax: the form or structure of the expressions, statements, and program units •Semantics: the meaning of the expressions, statements, and program units •Syntax and semantics provide a language’s definition – Users of a language definition •Other language designers •Implementers •Programmers (the users of the language) 1-3 The General Problem of Describing Syntax: Terminology •A sentence is a string of characters over some alphabet •A language is a set of sentences •A lexeme is the lowest level syntactic unit of a language (e.g., *, sum, begin) •A token is a category of lexemes (e.g., identifier) 1-4 Example: Lexemes and Tokens index = 2 * count + 17 Lexemes Tokens index identifier = equal_sign 2 int_literal * mult_op count identifier + plus_op 17 int_literal ; semicolon Formal Definition of Languages • Recognizers – A recognition device reads input strings over the alphabet of the language and decides whether the input strings belong to the language – Example: syntax analysis part of a compiler - Detailed discussion of syntax analysis appears in Chapter 4 • Generators – A device that generates sentences of a language – One can determine if the syntax of a particular sentence is syntactically correct by comparing it to the structure of the generator 1-5 Formal Methods of Describing Syntax •Formal language-generation mechanisms, usually called grammars, are commonly used to describe the syntax of programming languages. -
Static Vs. Dynamic Semantics (1) Static Vs
Why Does PL Semantics Matter? (1) Why Does PL Semantics Matter? (2) • Documentation • Language Design - Programmers (“What does X mean? Did - Semantic simplicity is a good guiding G54FOP: Lecture 3 the compiler get it right?”) Programming Language Semantics: principle - Implementers (“How to implement X?”) Introduction - Ensure desirable meta-theoretical • Formal Reasoning properties hold (like “well-typed programs Henrik Nilsson - Proofs about programs do not go wrong”) University of Nottingham, UK - Proofs about programming languages • Education (E.g. “Well-typed programs do not go - Learning new languages wrong”) - Comparing languages - Proofs about tools (E.g. compiler correctness) • Research G54FOP: Lecture 3 – p.1/21 G54FOP: Lecture 3 – p.2/21 G54FOP: Lecture 3 – p.3/21 Static vs. Dynamic Semantics (1) Static vs. Dynamic Semantics (2) Styles of Semantics (1) Main examples: • Static Semantics: “compile-time” meaning Distinction between static and dynamic • Operational Semantics: Meaning given by semantics not always clear cut. E.g. - Scope rules Abstract Machine, often a Transition Function - Type rules • Multi-staged languages (“more than one mapping a state to a “more evaluated” state. Example: the meaning of 1+2 is an integer run-time”) Kinds: value (its type is Integer) • Dependently typed languages (computation - small-step semantics: each step is • Dynamic Semantics: “run-time” meaning at the type level) atomic; more machine like - Exactly what value does a term evaluate to? - structural operational semantics (SOS): - What are the effects of a computation? compound, but still simple, steps Example: the meaning of 1+2 is the integer 3. - big-step or natural semantics: Single, compound step evaluates term to final value.