DOCSLIB.ORG

Using Semantics in Non-Context-Free of Montague Grammar

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Using Semantics in Non-Context-Free of Montague Grammar Using Semantics in Non-Context-Free Parsing of Montague Grammar 1 David Scott Warren Department of Computer Science SUNY at Stony Brook Long Island, NY 11794 Joyce Friedman University of Michigan Ann Arbor, MI In natural language processing, the question of the appropriate interaction of syntax and semantics during sentence analysis has long been of interest. Montague grammar with its fully formalized syntax and semantics provides a complete, well-defined context in which these questions can be considered. This paper describes how semantics can be used during parsing to reduce the combinatorial explosion of syntactic ambiguity in Montague grammar. A parsing algorithm, called semantic equivalence parsing, is presented and examples of its operation are given. The algorithm is applicable to general non-context-free grammars that include a formal semantic component. The second portion of the paper places semantic equivalence parsing in the context of the very general definition of an interpreted language as a homomorphism between syntactic and semantic algebras (Montague 1970). Introduction nondeterministic syntactic program expressed as an The close interrelation between syntax and seman- ATN. The algorithm introduces equivalence parsing, tics in Montague grammar provides a good framework which is a general execution method for nondetermin- in which to consider the interaction of syntax and istic programs that is based on a recall table, a gener- semantics in sentence analysis. Several different ap- alization of the well-formed substring table. Semantic proaches are possible in this framework and they can equivalence, based on logical equivalence of formulas obtained as translations, is used. We discuss the con- be developed rigorously for comparison. In this paper sequences of incorporating semantic processing into we develop an approach called semantic equivalence the parser and give examples of both syntactic and parsing that introduces logical translation into the on- semantic parsing. In Part II the semantic parsing al- going parsing process. We compare this with our ear- gorithm is related to earlier tabular context-free recog- lier directed process implementation in which syntactic nition methods. Relating our algorithm to its prede- parsing is completed prior to translation to logical cessors gives a new way of viewing the technique. form. The algorithmic description is then replaced by a de- Part I of the paper gives an algorithm that parses a scription in terms of refined grammars. Finally we class of grammars that contains both essentially suggest how this notion might be generalized to the context-free rules and non-context-free rules as in full class of Montague grammars. Montague's 1973 PTQ. Underlying this algorithm is a The particular version of Montague grammar used here is that of PTQ, with which the reader is assumed 1 A preliminary version of this paper was presented at the to be conversant. The syntactic component of PTQ is symposium on Modelling Human Parsing Strategies at the Universi- ty of Texas at Austin, March 24-26, 1981. The work of the first an essentially context-free grammar, augmented by author was supported in part by NSF grant IST 80-10834. some additional rules of a different form. The non- Copyright 1982 by the Association for Computational Linguistics. Permission to copy without fee all or part of this material is granted provided that the copies are not made for direct commercial advantage and the Journal reference and this copyright notice are included on the first page. To copy otherwise, or to republish, requires a fee and/or specific permission. 0362-613X/82/030123-16503.00 American Journal of Computational Linguistics, Volume 8, Number 3-4, July-December 1982 123 David Scott Warren and Joyce Friedman Using Semantics in Non-Context-Free Parsing context-free aspects arise in the treatment of quantifi- system (Gawron et al. 1982) and by Rosenschein and er scope and pronouns and their antecedents. Syntac- Shieber 1982. Neither of those systems treats pro- tically each antecedent is regarded as substituted into nouns. In Montague's approach, which we follow a place marked by a variable. This is not unlike the here, the trees produced by the parser are expressions way fillers are inserted into gaps in Gazdar's 1979 in the disambiguated language, so scope is determined, treatment. However, Montague's use of variables pronoun antecedents are indicated, and each tree has a allows complicated interactions between different unique (unreduced) translation. The descriptions of variable-antecedent pairs. Each substitution rule sub- the systems that use Cooper's approach seem to imply stitutes a term phrase (NP) for one or more occurrenc- that they use a second pass over the syntax tree to es of a free variable in a phrase (which may be a sen- determine the actual quantifier scopes in the final logi- tence, common noun phrase, or intransitive verb cal forms. Were these systems to use a single pass to phrase). The first occurrence of the variable is re- produce the final logical forms, the results described in placed by the phrase; later occurrences are replaced by this paper would be directly applicable. appropriate pronouns. The translation of the resulting phrase expresses the coreferentiality of the noun 1. Equivalence Parsing phrase and the pronouns. With substitution, but with- Ambiguity out pronouns, the only function of substitution is to determine quantifier scope. Ambiguity in Montague grammar is measured by the number of different meanings. In this view syn- Directed Process Approach tactic structure is of no interest in its own right, but only as a vehicle for mapping semantics. Syntactic One computational approach to processing a sen- ambiguity does not directly correspond to semantic tence is the directed process approach, which is a se- ambiguity, and there may be many parses with the quential analysis that follows the three-part presenta- same semantic interpretation. Further, sentences with tion in PTQ. The three steps are as follows. A purely scope ambiguity, such as A man loves every woman, syntactic analysis of a sentence yields a set of parse require more than one parse, because the syntactic trees, each an expression in the disambiguated lan- derivation determines quantifier scope. guage. Each parse tree is then translated by In PTQ there is infinite syntactic ambiguity arising Montague's rules into a formula of intentional logic to from three sources: alphabetic variants of variables, which logical reductions are immediately applied. The variable for variable substitutions, and vacuous varia- reduced formulas can then be interpreted in a model. ble substitution. However, these semantically unnec- The directed process approach is the one taken in the essary constructs can be eliminated, so that the set of system described by Friedman, Moran, and Warren syntactic sources for any sentence is finite, and a par- 1978a,b. ser that finds the full set is possible. (This corre- Semantic equivalence parsing is motivated by the sponds to the "variable principle" enunciated by Jans- observation that the directed process approach, in sen 1980 and used by Landsbergen 1980.) This ap- which all of the syntactic processing is completed be- proach was the basis of our earlier PTQ parser fore any semantic processing begins, does not take (Friedman and Warren 1978). maximal advantage of the coupling of syntax and se- However, even with these reductions the number of mantics in Montague grammars. Compositionality and remaining parses for a sentence of reasonable com- the fact that for each syntactic rule there is a transla- plexity is still large compared to the number of non- tion rule suggest that it would be possible to do a equivalent translations. In the directed process ap- combined syntactic-semantic parse. In this approach, proach this is treated by first finding all the parses, as soon as a subphrase is parsed, its logical formula is next finding for each parse a reduced translation, and obtained and reduced to an extensionalized normal then finally obtaining the set of reduced translations. form. Two parses for the same phrase can then be Each reduced translation may, but does not necessari- regarded equivalent if they have the same formula. ly, represent a different sentence meaning. No mean- The approach to parsing suggested by Cooper's ings are lost. Further reductions of the set of transla- 1975 treatment of quantified noun phrases is like our tions would be possible, but the undecidability of logi- semantic equivalence parsing in storing translations as cal equivalence precludes algorithmic reduction to a one element of the tuple corresponding to a noun minimal set. phrase. Cooper's approach differs from the approach followed here because he has an intermediate stage The ATN Program that might be called an "autonomous syntax tree". In the underlying parser the grammar is expressed The frontier of the tree is the sentence; the scope of as an augmented transition network (ATN) (Woods the quantifier of a noun phrase is not yet indicated. 1973). Both the syntactic and the semantic parsers Cooper's approach has been followed by the GPSG use this same ATN. The main difficulty in construct- 124 American Journal of Computational Linguistics, Volume 8, Number 3-4, July-December 1982 David Scott Warren and Joyce Friedman Using Semantics in Non-Context-Free Parsing ing the ATN was, as usual, the non-context-free as- need to rewrite the grammar to eliminate left-recursive pects of the grammar, in particular the incorporation rules as is usually necessary. of a treatment of substitution rules and variables. The In a general nondeterministic program, a bucket in grammar given in PTQ generates infinitely many deriv- the recall table corresponds to a particular subroutine ations for each sentence. All but finitely many of and a set of values for the calling parameters and re- these are unnecessary variations on variables and were turn parameters.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • Donkey Anaphora Is In-Scope Binding∗
    Semantics & Pragmatics Volume 1, Article 1: 1–46, 2008 doi: 10.3765/sp.1.1 Donkey anaphora is in-scope binding∗ Chris Barker Chung-chieh Shan New York University Rutgers University Received 2008-01-06 = First Decision 2008-02-29 = Revised 2008-03-23 = Second Decision 2008-03-25 = Revised 2008-03-27 = Accepted 2008-03-27 = Published 2008- 06-09 Abstract We propose that the antecedent of a donkey pronoun takes scope over and binds the donkey pronoun, just like any other quantificational antecedent would bind a pronoun. We flesh out this idea in a grammar that compositionally derives the truth conditions of donkey sentences containing conditionals and relative clauses, including those involving modals and proportional quantifiers. For example, an indefinite in the antecedent of a conditional can bind a donkey pronoun in the consequent by taking scope over the entire conditional. Our grammar manages continuations using three independently motivated type-shifters, Lift, Lower, and Bind. Empirical support comes from donkey weak crossover (*He beats it if a farmer owns a donkey): in our system, a quantificational binder need not c-command a pronoun that it binds, but must be evaluated before it, so that donkey weak crossover is just a special case of weak crossover. We compare our approach to situation-based E-type pronoun analyses, as well as to dynamic accounts such as Dynamic Predicate Logic. A new ‘tower’ notation makes derivations considerably easier to follow and manipulate than some previous grammars based on continuations. Keywords: donkey anaphora, continuations, E-type pronoun, type-shifting, scope, quantification, binding, dynamic semantics, weak crossover, donkey pronoun, variable-free, direct compositionality, D-type pronoun, conditionals, situation se- mantics, c-command, dynamic predicate logic, donkey weak crossover ∗ Thanks to substantial input from Anna Chernilovskaya, Brady Clark, Paul Elbourne, Makoto Kanazawa, Chris Kennedy, Thomas Leu, Floris Roelofsen, Daniel Rothschild, Anna Szabolcsi, Eytan Zweig, and three anonymous referees.
    [Show full text]
  • Montague Grammar Induction*
    Proceedings of SALT 30: 000–000, 2020 Montague Grammar Induction* Gene Louis Kim Aaron Steven White University of Rochester University of Rochester Abstract We propose a computational modeling framework for inducing combina- tory categorial grammars from arbitrary behavioral data. This framework provides the analyst fine-grained control over the assumptions that the induced grammar should conform to: (i) what the primitive types are; (ii) how complex types are constructed; (iii) what set of combinators can be used to combine types; and (iv) whether (and to what) the types of some lexical items should be fixed. In a proof- of-concept experiment, we deploy our framework for use in distributional analysis. We focus on the relationship between s(emantic)-selection and c(ategory)-selection, using as input a lexicon-scale acceptability judgment dataset focused on English verbs’ syntactic distribution (the MegaAcceptability dataset) and enforcing standard assumptions from the semantics literature on the induced grammar. Keywords: grammar induction, combinatory categorial grammar, semantic selection, ex- perimental semantics, computational semantics, experimental syntax, computational syntax 1 Introduction Semantic theories aim to capture two kinds of facts about languages’ expressions: (i) their distributional characteristics; and (ii) their inferential affordances. The descriptive adequacy of any such theory is evaluated in terms of its coverage of these facts—an evaluation that is commonly carried out informally on a relatively small number of test cases. While this approach to theory-building and evaluation has yielded deep insights, it also carries significant risks: generalizations that appear arXiv:2010.08067v1 [cs.CL] 15 Oct 2020 unassailable based a small number of high-frequency examples (and theories built on them) can collapse when evaluated on a more diverse range of expressions purportedly covered by the generalization (see White accepted for recent discussion).
    [Show full text]
  • Lecture 2. Lambda Abstraction, NP Semantics, and a Fragment of English
    Formal Semantics, Lecture 2 Formal Semantics, Lecture 2 B. Partee, MGU, February 22, 2005 p.1 B. Partee, MGU, February 22, 2005 p.2 Lecture 2. Lambda abstraction, NP semantics, and a Fragment of English (b) NP 1. Lexical and Structural Ambiguity..............................................................................................................................1 | 2. Lambdas ....................................................................................................................................................................3 CNP 2.1. A first-order part of the lambda-calculus............................................................................................................3 3 2.2. The typed lambda calculus. ................................................................................................................................4 ADJ CNP 3. Montague’s semantics for Noun Phrases...................................................................................................................5 | 3.1. Semantics via direct model-theoretic interpretation of English..........................................................................5 9 3.2. Semantics via translation from English into a logical language. ........................................................................5 old CNP and CNP 4. English Fragment 1...................................................................................................................................................5 | | 4.0 Introduction ........................................................................................................................................................5
    [Show full text]
  • Questions and Answers in a Context-Dependent Montague Grammar 339 WALTHER KINDT / the Introduction of Truth Predicates Into First-Order Languages 359
    SYNTHESE LANGUAGE LIBRARY TEXTS AND STUDIES IN LINGUISTICS AND PHILOSOPHY Managing Editors: JAAKKO HINTIKKA, Academy of ¥ Inland and Stanford University STANLEY PETERS, The University of Texas at Austin Editorial Board: EMMON BACH, University of Massachusetts at Amherst JOAN BRESNAN, Massachusetts Institute of Technology JOHN LYONS, University of Sussex JULIUS M. E. MORAVCSIK, Stanford University PATRICK SUPPES, Stanford University DANA SCOTT, Oxford University VOLUME 4 FORMAL SEMANTICS AND PRAGMATICS FOR NATURAL LANGUAGES Edited by F. GUENTHNER Universität Tübingen, Seminar für Englische Philologie, Tübingen, B.R.D. and S. J. SCHMIDT Universität Bielefeld, B.R.D. D. REIDEL PUBLISHING COMPANY DORDRECHT : HOLLAND / BOSTON : U.S.A. LONDON:ENGLAND Library of Congress Cataloging in Publication Data Main entry under title: UP Formal semantics and pragmatics for natural languages. (Synthese language library; v. 4) "Essays in this collection are the outgrowth of a Workshop held in June 1976." Includes bibliographies and index. 1. Languages — Philosophy. 2. Semantics. 3. Pragmatics. 4. Predicate calculus. 5. Tense (Logic). 6. Grammar, Comparative and general. I. Guenthner, Franz. II. Schmidt, S. J., 1941- III. Series. P106.F66 401 78-13180 ISBN 90-277-0778-2 ISBN 90-277-0930-0 pbk. Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. f Bayerische j I Staatsbibliothek
    [Show full text]
  • Montague's PTQ: Synthese Language Library
    Montague’s “Linguistic” Work: Motivations, Trajectory, Attitudes Barbara Partee – University of Massachusetts, Amherst Abstract. The history of formal semantics is a history of evolving ideas about logical form, linguistic form, and the nature of semantics (and pragmatics). This paper discusses Montague’s work in its historical context, and traces the evolution of his interest in issues of natural language, including the emergence of his interest in quantified noun phrases from a concern with intensional transitive verbs like seeks. Drawing in part on research in the Montague Archives in the UCLA Library, I discuss Montague’s motivation for his work on natural language semantics, his evaluation of its importance, and his evolving ideas about various linguistic topics, including some that he evidently thought about but did not include in his published work. Keywords: formal semantics, formal pragmatics, history of semantics, Richard Montague, Montague grammar, logical form, linguistic form, intensional verbs, generalized quantifiers. 1. Introduction The history of formal semantics is a history of evolving ideas about logical form, linguistic form, and the nature of semantics (and pragmatics). This paper1 discusses Montague’s work in its historical context, and traces the evolution of his interest in issues of natural language, including the emergence of his interest in quantified noun phrases from a concern with intensional transitive verbs like seeks. Drawing in part on research in the archived Montague papers in the UCLA Library, I discuss Montague’s motivation for his work on natural language semantics, his evaluation of its importance, and his evolving ideas about various linguistic topics, including some that he evidently thought about but did not include in his published work.
    [Show full text]
  • Richard Montague and the Logical Analysis of Language
    Richard Montague and the Logical Analysis of Language Nino B. Cocchiarella Richard Montague was an exceptionally gifted logician who made im- portant contributions in every …eld of inquiry upon which he wrote. His professional career was not only marked with brilliance and insight but it has become a classic example of the changing and developing philosophical views of logicians in general, especially during the 1960s and 70s, in regard to the form and content of natural language. We shall, in what follows, at- tempt to characterize the general pattern of that development, at least to the extent that it is exempli…ed in the articles Montague wrote during the period in question. The articles to which we shall especially direct our attention are: ‘Prag- matics’[1]; ‘Pragmatics and Intensional Logic’[2]; ‘On the Nature of Certain Philosophical Entities’ [3]; ‘English as a Formal Language’ [4]; ‘Universal Grammar’ [5]; and ‘The Proper Treatment of Quanti…cation in Ordinary English’[7]. Needless to say, but many of the ideas and insights developed in these papers Montague shared with other philosophers and logicians, some of whom were his own students at the times in question. Montague himself was meticulous in crediting others where credit was due, but for convenience we shall avoid duplicating such references here. 1 Constructed Versus Natural Languages In his earlier pre-1964 phase of philosophical development Montague thought a formalization of English or any of natural language was either impossible or extremely laborious and not rewarding ([10], p. 10). In his view there was an important di¤erence between constructing a formal language for the purpose of analyzing concepts that were of interest to philosophers and investigating the behavior of the expressions in natural language that were ordinarily used 1 to express those concepts.
    [Show full text]
  • Modularity and Compositionality: the Case of Temporal Modifiers
    Proceedings of SALT 25: 656–675, 2015 Modularity and compositionality: The case of temporal modifiers ∗ Philippe de Groote Inria Abstract This paper concerns the possibility of building Montague grammars in a modular and incremental way. As an illustration, we investigate the following question: Given an atemporal Montague grammar, on the one hand, and a temporal ontology, on the other hand, is it possible to combine them into a new grammar such that it would: (i) conservatively extend the original grammar, and (ii) allow temporal modifiers to be accommodated? Keywords: compositionality, modularity, temporal prepositional phrases 1 Introduction One says that a semantics is compositional when it allows the meaning of a complex expression to be computed from the meaning of its constituents. One also says that a system is modular if it is made of relatively independent components. In the case of a semantic system, say a Montague grammar, we will say that it is modular if the ontology on which it is based (including notions such as truth, entities, events, possible worlds, time intervals, state of knowledge, state of believe, ...) is obtained by combining relatively independent simple ontologies. We believe that modularity is a requirement as important as compositionality. A large semantic system that is not be modular would be quite difficult to grasp and present little explanatory power. In addition, modularity plays an essential part in the incremental development of a semantic system. Typically, in the absence of modularity, when studying a new semantic phenomenon, it is problematic to decide whether and how the proposed treatment is compatible with the treatments of other phenomena.
    [Show full text]
  • Alternatives in Montague Grammar∗
    Alternatives in Montague Grammar∗ Ivano Ciardelli Floris Roelofsen Abstract The type theoretic framework for natural language semantics laid out by Montague (1973) forms the cornerstone of formal semantics. Hamblin (1973) proposed an extension of Mon- tague's basic framework, referred to as alternative semantics. In this framework, the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions|a set of alternatives. While this more fine-grained view on meaning has led to improved analyses of a wide range of linguistic phenomena, it also faces a number of problems. We focus here on two of these, in our view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstrac- tion; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin's proposal with the solid type-theoretic foundations of Montague grammar, in such a way that the observed problems evaporate. Our proposal partly builds on insights from recent work on inquisitive semantics (Ciardelli et al., 2013), and it also further advances this line of work, specifying how the inquisitive meaning of a sentence, as well as the set of alternatives that it introduces, may be built up compositionally. 1 Introduction Alternative semantics (Hamblin, 1973; Rooth, 1985; Kratzer and Shimoyama, 2002, among others) diverges from the standard, Montagovian framework for natural language semantics in that the semantic value of an expression is taken to be a set of objects in the expression's usual domain of interpretation, rather than a single object.
    [Show full text]
  • Structural Ambiguity in Montague Grammar and Categorial Grammar
    Structural Ambiguity in Montague Grammar and Categorial Grammar Glyn Morrill Departament de Llenguatges i Sistemes Inform`atics Universitat Polit`ecnicade Catalunya [email protected] http://www.lsi.upc.edu/~morrill/ Abstract We give a type logical categorial grammar for the syntax and semantics of Montague's seminal fragment, which includes ambiguities of quantification and intensionality and their interactions, and we present the analyses assigned by a parser/theorem prover CatLog to the examples of the first half of Chapter 7 of the classic text Introduction to Montague Semantics of Dowty, Wall and Peters (1981). Keywords: categorial grammar, displacement calculus, intensionality, modal categorial logic, Montague Grammar, parsing as deduction, quantification, type logical grammar. 1 Introduction Logical semantics came into being with Montague Grammar: Montague (1970b) (UG), Montague (1970a) (EFL), and Montague (1973) (PTQ), which introduced into linguistics tools like lambda calculus and intensional logic, and algebraic compositionality, and exemplified the paradigm with a grammar for a well-known fragment including quantification, intensionality and anaphora and, significantly, their interactions. Type logical categorial grammar reduces grammar to logic: an expression is grammatical if and only if an associated sequent is a theorem (Moortgat 1988; Morrill 1994; Moortgat 1997; Carpenter 1997; J¨ager2005; Morrill 2011b; Moot and Retor´e2012). In such categorial grammar type-logical semantics is assigned by the constructive reading of a syntactic proof as a semantic lambda term. In this paper we consider type logical categorial grammar for the Montague fragment. The conventional understanding is that grammar should assign \structural descriptions" to grammatical sentences, and that where there is structural ambiguity there should be multiple structural descriptions corresponding to the different readings.
    [Show full text]