DOCSLIB.ORG

A Natural Proof System for Natural Language

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Natural Proof System for Natural Language A In the �tle of this thesis, a proof system refers to a system that carries out formal proofs (e.g., of theorems). Logicians would interpret a system as a symbolic calculus while com- Natural puter scien�sts might understand it as a computer program. Both interpreta�ons are fine for the current purpose as the thesis develops a proof calculi and a computer program A NATURAL PROOF SYSTEM based on it. What makes the proof system natural is that it operates on formulas with a natural appearance, i.e. resembling natural language phrases. This is contrasted to the Proof artificial formulas logicians usually use. Put differently, the natural proof system is FOR NATURAL LANGUAGE designed for a natural logic, a logic that has formulas similar to natural language sentenc- es. The natural proof system represents a further development of an analy�c tableau system for natural logic (Muskens, 2010). The implementa�on of the system acts as a System pp theorem prover for wide-coverage natural language sentences. For instance, it can prove x n that not all PhD theses are interesting entails some dissertations are not interesting. On z certain textual entailment datasets, the prover achieves results compe��ve to the y s state-of-the-art. t γT pp for zγ αF s Natural vp x t β e s vp t T F e np t s n e Language y z λ e s T t T z γ α z λα t n x e F e s T npα λ γ t x β y pp T pp y np x t γ e T n λ T s e x γ t T z F λ z y γ t T s e z e λ αn s β t T np α λ λ e F t α γ Lasha Abzianidze vp x s e s t vp pp F λ s y t z z T λ β n x αpp γ Lasha Abzianidze γ ISBN 978-94-6299-494-2 A Natural Proof System for Natural Language ISBN 978-94-6299-494-2 cb 2016 by Lasha Abzianidze Cover & inner design by Lasha Abzianidze Used item: leaf1 font by Rika Kawamoto Printed and bound by Ridderprint BV, Ridderkerk A Natural Proof System for Natural Language Proefschrift ter verkrijging van de graad van doctor aan Tilburg University op gezag van de rector magnificus, prof.dr. E.H.L. Aarts, in het openbaar te verdedigen ten overstaan van een door het college voor promoties aangewezen commissie in de aula van de Universiteit op vrijdag 20 januari 2017 om 14.00 uur door Lasha Abzianidze geboren op 24 januari 1987 te Tbilisi, Georgie¨ Promotiecommissie Promotor Prof. dr. J.M. Sprenger Copromotor Dr. R.A. Muskens Overige leden Prof. dr. Ph. de Groote Dr. R. Moot Prof. dr. L.S. Moss Prof. dr. Y. Winter Acknowledgments During working on this dissertation, there were many people who helped and supported me, both inside and outside the academic life. Here I would like to thank them. First, my sincere thanks go to my supervisors Jan and Reinhard. I learned a lot from them during this period. Their joint feedback and guidance were vital for my research. This dissertation would not have been possible without their input. Many thanks go to Reinhard who believed that I was a suitable candidate for his innovative research program. He continuously provided me with crucial advice and suggestions during the research. I thank him for believing in me and giving me a freedom to choose a more exciting and demanding research direction towards wide-coverage semantics. Jan gave me valuable and needed support in the later stage of the project. His comments and suggestions have significantly improved the presentation in the thesis. I also benefited from his advice about job applications. I am grateful to him. I feel very lucky to have so much expertise and leading researchers of my field on the committee. I am thankful to Philippe de Groote, Richard Moot, Larry Moss and Yoad Winter for that. Additionally, I am indebted to Philippe for his support during my LCT master study, and I want express my gratitude to Larry whose comments and opinion on my work has been inspiring. Special thanks go to my office mate Janine and my close friend Irakli who agreed to be my paranymphs. I also thank Janine for preparing delicious cakes and sweets for me. Irakli has been a friend I can rely on any time. I appreciate it. I acknowledge the valuable benefit and feedback I got from participating in several ESSLLI schools, attending and presenting at several workshops and conferences, among them LENLS, WoLLIC, EMNLP, TbiLLC, Amsterdam Colloquium, ACL and *SEM. The local TiLPS seminars were very helpful, where I presented early results of my re- search and widened my knowledge of logic, language and philosophy. My working environment and stay in Tilburg were enjoyable due to my colleagues at TiLPS: Alessandra, Alfred, Barbara, Bart, Chiara, Colin, Dominik, Georgi, Jan, Janine, Jasmina, Jun, Silvia, Machteld, Matteo, Michal, Naftali, Reinhard, and Thomas. Thank you guys; with you I enjoyed playing footy in the corridor, having drinks, dinners or parties, watching football, going on TiLPS excursions, or simply spending time together. I also want to thank my close friend Sandro, who was also doing his PhD meanwhile. The (skype) conversations with him were helpful, encouraging and entertaining for me. Many thanks go to my family on the other side of the continent. Especially I want to thank my mother, who always did her best to support and create conditions for me to feel comfortable and to concentrate on my studies. I am deeply grateful to her for everything. Finally and mostly, I would like to thank mu kallis Eleri for her continuous and endless support, patience and unconditional love during this period. She bared me when I was obsessed with research and writing. Her help and care have been indispensable for me. I cannot thank her enough. v vi Abstract We humans easily understand semantics of natural language text and make inferences based on it. But how can we make machines reason and carry out inferences on the text? The question represents a crucial problem for several research fields and is at the heart of the current thesis. One of the most intuitive approaches to model reasoning in natural language is to translate semantics of linguistic expressions into some formal logic that comes with an automated inference procedure. Unfortunately, designing such automatized translation turns out to be almost as hard as the initial problem of reasoning. In this thesis, following Muskens(2010), we develop a model for natural reasoning that takes a proof theoretic stand. Instead of a heavy translation procedure, we opt for a light-weight one. Logical forms obtained after the translation are natural in the sense that they come close to the original linguistic expressions. But at the same time, they represent terms of higher-order logic. In order to reason over such logical forms, we extend a tableau proof system for type theory by Muskens. An obtained natural tableau system employs inference rules specially tailored for various linguistic constructions. Since we employ the logical forms close to linguistic expressions, our approach con- tributes to the project of natural logic. Put differently, we employ the higher-order logic disguised as natural logic. Due to this hybrid nature, the proof system can carry out both shallow and deep reasoning over multiple-premised arguments. While doing so, a main vehicle for shallow reasoning is monotonicity calculus. In order to evaluate the natural proof system, we automatize it as a theorem prover for wide-coverage natural language text. In particular, first the logical forms are obtained from syntactic trees of linguistic expressions, and then they are processed by the prover. Despite its simple architecture, on certain textual entailment benchmarks the prover ob- tains high competitive results for both shallow and deep reasoning. Notice that this is done while it employs only WordNet as a knowledge base. The theorem prover also rep- resents the first wide-coverage system for natural logic which can reason over multiple propositions at the same time. The thesis makes three major contributions. First, it significantly extends the natu- ral tableau system for wide-coverage natural reasoning. After extending the type system and the format of tableau entries (Chapter 2), we collect a plethora of inference rules for a wide range of constructions (Chapter 4). Second, the thesis proposes a procedure to obtain the logical forms from syntactic derivations of linguistic expressions (Chapter 3). The procedure is anticipated as a useful tool for wide-coverage compositional semantic analysis. Last, based on the natural tableau system, the theorem prover for natural lan- guage is implemented (Chapter 5,6). The prover represents a state-of-the-art system of natural logic. vii viii Contents Acknowledgmentsv Abstract vii 1 Introduction1 1.1 Natural language inference.........................1 1.2 Overview of approaches to textual entailment...............4 1.3 Natural logic and monotonicity.......................7 1.4 Natural logic approach to textual entailment................ 10 1.5 Overview of what follows.......................... 13 2 Natural Tableau for Natural Reasoning 15 2.0 Preliminaries................................ 15 2.0.1 Functional type theory....................... 16 2.0.2 Semantic tableau method...................... 20 2.1 An analytic tableau system for natural logic................ 23 2.2 Extending the type system......................... 32 2.3 Extending the tableau entries........................ 35 2.3.1 Event semantics and LLFs..................... 36 2.3.2 Modifier list and event semantics.................. 38 2.4 Extending the inventory of rules...................... 41 2.4.1 Rules for modifiers and the memory list.............
Load more

Recommended publications
  • (Syntax)–Semantics Part Two
    Current Issues in Generative Linguistics Syntax, Semantics, and Phonology edited by Joanna Błaszczak, Bożena Rozwadowska, and Wojciech Witkowski Contents About this volume part one: syntax Generative Linguistics in Wrocław (GLiW) series is published by the Center Ángel l. Jiménez-FernÁndez and Selçuk İşSever for General and Comparative Linguistics, a unit of the Institute of English at the University of Wrocław. Deriving A/A’-Effects in Topic Fronting: Intervention of Focus and Binding Address: nataša knežević Center for General and Comparative Linguistics (CGCL) Serbian Distributive Children ul. Kuźnicza 22 50-138 Wrocław, Poland Slavica kochovSka Two Kinds of Dislocated Topics in Macedonian about the series: Generative Linguistics in Wrocław (GLiW) is meant to provide a suitable forum for the presentation and discussion of the Pol- katarzyna miechowicz-mathiaSen ish research within the field of generative linguistics. We are interested in Licensing Polish Higher Numerals: An Account of the Accusative Hypothesis studies that employ generative methodology to the synchronic or diachronic analysis of phonology, semantics, morphology, and syntax. Apart from that, kathleen m. o’connor we express a keen interest in interdisciplinary research that is based on typol- On the Positions of Subjects and Floating Quantifiers in Appositives ogy, diachrony, and especially experimental methods taken from psycho- or neurolinguistics and applied so as to provide a psycholinguistic background yurie okami to purely theoretical research. We believe that the dissemination of ideas is Two Types of Modification and the Adnominal Modification in Japanese fundamental to any scientific advancement and thus our choice is to publish research studies in the form of ebooks, available for free on our website.
    [Show full text]
  • Person Features: Deriving the Inventory of Persons
    Chapter 2 Person Features: Deriving the Inventory of Persons 1. Introduction One long-standing aim of research into person has been to achieve a deeper understanding of the inventory of personal pronouns by decomposing them into a limited set of person features. The main aim of this chapter is to make a contribution to this enterprise. We will argue that a set of two privative person features is sufficient to derive the full inventory of attested pronouns and their interpretations, without generating non-attested pronouns. In chapter 1 we showed that the cross-linguistic inventory of attested persons is a small subset of the set of theoretically possible persons. The theoretically possible persons are those that can be formed by freely combining the speaker (for which we use the symbol i), associates of the speaker (ai), the addressee (u), associates of the addressee (au), and others (o). The generalizations that distinguish between the attested and non-attested persons are the following (repeated from (9) in chapter 1): (1) a. There is no person that contains associates of a participant but not the participant itself. b. There is no person that consists of others and only speaker(s) or of others and only addressee(s). c. No person system distinguishes pluralities containing a participant but not its associates from pluralities containing that participant as well as its associates. d. First and second person plural pronouns show an ‘associative effect’: any element contained in them other than i or u must be ai or au and cannot be o. 31 This leaves us with three persons with a singular interpretation and four persons with a plural interpretation.
    [Show full text]
  • Cross-Linguistic Representations of Numerals and Number Marking∗
    Proceedings of SALT 20: 582–598, 2011 Cross-linguistic representations of numerals and number marking∗ Alan Bale Michaël Gagnon Concordia University University of Maryland Hrayr Khanjian Massachusetts Institute of Technology Abstract Inspired by Partee(2010), this paper defends a broad thesis that all mod- ifiers, including numeral modifiers, are restrictive in the sense that they can only restrict the denotation of the NP or VP they modify. However, the paper concentrates more narrowly on numeral modification, demonstrating that the evidence that moti- vated Ionin & Matushansky(2006) to assign non-restrictive, privative interpretations to numerals – assigning them functions that map singular sets to sets containing groups – is in fact consistent with restrictive modification. Ionin & Matushansky’s (2006) argument for this type of interpretation is partly based on the distribution of Turkish numerals which exclusively combine with singular bare nouns. Section 2 demonstrates that Turkish singular bare nouns are not semantically singular, but rather are unspecified for number. Western Armenian has similar characteristics. Building on some of the observations in section2, section3 demonstrates that re- strictive modification can account for three different types of languages with respect to the distribution of numerals and plural nouns: (i) languages where numerals exclusively combine with plural nouns (e.g., English), (ii) languages where they exclusively combine with singular bare nouns (e.g., Turkish), (iii) languages where they optionally combine with either type of noun (e.g., Western Armenian). Ac- counting for these differences crucially involves making a distinction between two kinds of restrictive modification among the numerals: subsective vs. intersective modification. Section3 also discusses why privative interpretations of numerals have trouble accounting for these different language types.
    [Show full text]
  • Ellipsis in Comparatives
    TITEL$0733 25-06-04 10:21:40 Titelei: SGG 72, Lechner META-Systems Ellipsis in Comparatives ≥ Studies in Generative Grammar 72 Editors Henk van Riemsdijk Harry van der Hulst Jan Koster Mouton de Gruyter Berlin · New York Ellipsis in Comparatives by Winfried Lechner Mouton de Gruyter Berlin · New York Mouton de Gruyter (formerly Mouton, The Hague) is a Division of Walter de Gruyter GmbH & Co. KG, Berlin. The series Studies in Generative Grammar was formerly published by Foris Publications Holland. Țȍ Printed on acid-free paper which falls within the guidelines of the ANSI to ensure permanence and durability. ISBN 3-11-018118-5 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at Ͻhttp://dnb.ddb.deϾ. Ą Copyright 2004 by Walter de Gruyter GmbH & Co. KG, D-10785 Berlin. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Printed in Germany. Acknowledgments This book profited greatly from many stimulating discussions with and con- structive comments by numerous linguists. I would like to express my grati- tude for their invaluable contributions at various stages of this project to: Artemis Alexiadou, Elena Anagnostopoulou, Rajesh Bhatt, Jonathan
    [Show full text]
  • Integrating Type Theory and Distributional Semantics: a Case Study on Adjective–Noun Compositions
    Integrating Type Theory and Distributional Semantics: A Case Study on Adjective–Noun Compositions Nicholas Asher∗ CNRS ∗ Tim Van de Cruys CNRS ∗ Antoine Bride Universit´e Paul Sabatier M´arta Abrus´an∗ CNRS In this article, we explore an integration of a formal semantic approach to lexical meaning and an approach based on distributional methods. First, we outline a formal semantic theory that aims to combine the virtues of both formal and distributional frameworks. We then proceed to develop an algebraic interpretation of that formal semantic theory and show how at least two kinds of distributional models make this interpretation concrete. Focusing on the case of adjective–noun composition, we compare several distributional models with respect to the semantic information that a formal semantic theory would need, and we show how to integrate the information provided by distributional models back into the formal semantic framework. 1. Introduction Formal semantics (FS) has provided insightful models of composition and recently has addressed issues of how composition may in turn affect the original meanings of lexical items (Pustejovsky 1995; Partee 2010; Asher 2011). Type Composition Logic (TCL; Asher 2011) provides a detailed formal model of the interaction between composition and lexical meaning in which the composition of two words w and w may shift the original meanings of w and w . For example, consider the case of an adjective like heavy and a noun like traffic. TCL assigns a logical form to the adjective–noun combination heavy traffic, λx.(O(heavy)(x) ∧ M(traffic)(x)), where O is a functor induced by the noun that outputs a meaning paraphrased as heavy for traffic.TheM functor does something ∗ IRIT, Universit´e Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 9.
    [Show full text]
  • MOSAIC 2 the Meeting of Semanticists Active in Canada Post-CLA Semantics Workshop
    MOSAIC 2 The Meeting of Semanticists Active in Canada Post-CLA semantics workshop June 1, 2010, McGill University Ball Room, Thomson House (David Thomson Post-Graduate Centre), 3650 McTavish Street, Montréal 8:30 Registration and coffee/muffins Session 1 (chair: Keir Moulton, McGill University) 9:00-10:00 Invited talk Epistemic Modals: Embedded, Modified, and Plain Angelika Kratzer (University of Massachusetts, Amherst) 10:00-10:30 Imperfective Values Ana Arregui and Maria Luisa Rivero (University of Ottawa) 10:30-10:50 Break Session 2 (chair: Walter Pederson, McGill University) 10:50-11:20 A Note on Ignorance Inferences Raj Singh (Carleton University) 11:20-11:50 Variable Binding, Reconstruction and Attitudes Keir Moulton (McGill University) 11:50-12:20 Numerals and Number Marking in English, Turkish and Armenian Alan Bale (Concordia University), Hrayr Khanjian (MIT) and Michaël Gagnon (University of Maryland) 12:20-1:50 Lunch at Thomson House for those who are registered online by one week before the workshop Session 3 (chair: Masako Hirotani, Carleton University) 1:50-2:50 Invited talk Distinguishing Contrastive, New and Given Information (joint work with Angelika Kratzer) Elisabeth Selkirk (University of Massachusetts, Amherst) 2:50-3:20 The Semantic Function of Rising Wh-Questions Nancy Hedberg and Morgan Mameni (Simon Fraser University) 3:20-3:40 Break Session 4 (chair: David-Étienne Bouchard, McGill University) 3:40-4:10 Blackfoot ikak-: A Case Study in 'Only' and 'Even' Heather Bliss (University of British Columbia) 4:10-4:40 Focus Sensitivity in Nlhe7kepmxcin (Thompson Salish) Karsten Koch (ZAS, Berlin) and Malte Zimmermann (Universität Potsdam) 4:40-5:10 Conjectural Questions and the Wonder Effect Patrick Littell (University of British Columbia) 5:30-7:00 Dinner arrangements for interested people Please register here by Thursday, May 27.
    [Show full text]
  • Semantics and Linguistic Theory (SALT) 20 April 29 - May 1, 2010 University of British Columbia and Simon Fraser University Vancouver, BC, Canada
    Semantics and Linguistic Theory (SALT) 20 April 29 - May 1, 2010 University of British Columbia and Simon Fraser University Vancouver, BC, Canada Collected Abstracts Invited Speakers A possible worlds semantics for (illocutionary) evidentials Martina Faller The precise relationship between evidentiality, the linguistic marking of the speaker's source of information for a claim, and epistemic modality, the marking of the speaker's evaluation of the truth of a proposition in terms of necessity, possibility or degree of certainty, is not yet fully understood. While these two phenomena are clearly distinct conceptually, it is not always possible to establish two distinct categories empirically in a given language because the two concepts are often expressed simultaneously by a single element. For example, English epistemic must expresses that the speaker s considers the proposition expressed p a necessity and in addition indicates that s has inferred p and does not have direct evidence for it. The two concepts are furthermore closely related in that the type of source information a speaker has will to a great extent determine the speaker's evaluation of the truth of the proposition. Within formal semantics, evidentials are often analyzed as quantifiers over possible worlds with evidential presuppositions, that is, as a kind of epistemic modal. In this talk I will explore to what extent such an analysis is viable for evidentials that do not contribute to the main proposition expressed/at-issue content such as the evidentials of Cuzco Quechua (CQ). CQ has four evidentials which I have ananlyzed in previous work as contributing to the illocutionary level of meaning.
    [Show full text]
  • A Case Study on Adjective–Noun Compositions
    Integrating Type Theory and Distributional Semantics: A Case Study on Adjective–Noun Compositions Nicholas Asher∗ CNRS ∗ Tim Van de Cruys CNRS ∗ Antoine Bride Universit´e Paul Sabatier M´arta Abrus´an∗ CNRS In this article, we explore an integration of a formal semantic approach to lexical meaning and an approach based on distributional methods. First, we outline a formal semantic theory that aims to combine the virtues of both formal and distributional frameworks. We then proceed to develop an algebraic interpretation of that formal semantic theory and show how at least two kinds of distributional models make this interpretation concrete. Focusing on the case of adjective–noun composition, we compare several distributional models with respect to the semantic information that a formal semantic theory would need, and we show how to integrate the information provided by distributional models back into the formal semantic framework. 1. Introduction Formal semantics (FS) has provided insightful models of composition and recently has addressed issues of how composition may in turn affect the original meanings of lexical items (Pustejovsky 1995; Partee 2010; Asher 2011). Type Composition Logic (TCL; Asher 2011) provides a detailed formal model of the interaction between composition and lexical meaning in which the composition of two words w and w may shift the original meanings of w and w . For example, consider the case of an adjective like heavy and a noun like traffic. TCL assigns a logical form to the adjective–noun combination heavy traffic, λx.(O(heavy)(x) ∧ M(traffic)(x)), where O is a functor induced by the noun that outputs a meaning paraphrased as heavy for traffic.TheM functor does something ∗ IRIT, Universit´e Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 9.
    [Show full text]
  • Tilburg University a Natural Proof System for Natural Language
    Tilburg University A Natural Proof System for Natural Language Abzianidze, Lasha Publication date: 2017 Document Version Publisher's PDF, also known as Version of record Link to publication in Tilburg University Research Portal Citation for published version (APA): Abzianidze, L. (2017). A Natural Proof System for Natural Language. Ridderprint. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 04. okt. 2021 A In the �tle of this thesis, a proof system refers to a system that carries out formal proofs (e.g., of theorems). Logicians would interpret a system as a symbolic calculus while com- Natural puter scien�sts might understand it as a computer program. Both interpreta�ons are fine for the current purpose as the thesis develops a proof calculi and a computer program A NATURAL PROOF SYSTEM based on it. What makes the proof system natural is that it operates on formulas with a natural appearance, i.e.
    [Show full text]
  • Two Kinds of Procedural Semantics for Privative Modification
    Two kinds of procedural semantics for privative modification Giuseppe Primiero1? and Bjørn Jespersen2?? 1 Centre for Logic and Philosophy of Science, Ghent University (Belgium) [email protected] 2 Department of Computer Science, Technical University of Ostrava; Institute of Philosophy, Department of Logic, Czech Academy of Sciences, Prague (Czech Republic) [email protected] Abstract. In this paper we present two kinds of procedural semantics for privative modification. We do this for three reasons. The first reason is to launch a tough test case to gauge the degree of substantial agree- ment between a constructivist and a realist interpretation of procedural semantics; the second is to extend Martin-L¨of's Constructive Type The- ory to privative modification, which is characteristic of natural language; the third reason is to sketch a positive characterization of privation. 1 Introduction The verbal agreements between constructivist/idealist and platonist/realist se- mantics are so numerous and so striking that it is worth exploring the extent to which there is also substantial agreement. This paper explores some of the common ground shared by the Constructive Type Theory of Per Martin-L¨of3 and the realist Transparent Intensional Logic of Pavel Tich´y.4 We focus here on the following common features: { a notion of construction; { a functional language; { a typed universe; { an interpreted syntax. These four features are sufficient to underpin a neutral notion of procedural semantics. Phrased in neutral terms, linguistic meaning is construed as an ab- stract procedure, of one or more steps, delineating what operations to apply to what operands in order to obtain a particular product as its outcome.
    [Show full text]
  • Realist and Constructivist Semantics for Modal Modification
    Alleged assassins: realist and constructivist semantics for modal modification Bjørn Jespersen1? and Giuseppe Primiero2?? 1 Institute of Philosophy, Department of Logic, Czech Academy of Sciences, Prague; Department of Computer Science, Technical University of Ostrava (Czech Republic) [email protected] 2 Centre for Logic and Philosophy of Science, Ghent University (Belgium) [email protected] Abstract. Modal modifiers such as Alleged oscillate between being sub- sective and being privative. If individual a is an alleged assassin (at some parameter of evaluation) then it is an open question whether a is an assassin (at that parameter). Standardly, modal modifiers are nega- tively defined, in terms of failed inferences or non-intersectivity or non- extensionality. Modal modifiers are in want of a positive definition and a worked-out logical semantics. This paper offers two positive definitions. The realist definition is elaborated within Tich´y'sTransparent Inten- sional Logic (TIL) and builds upon Montague's model-theoretic seman- tics for adjectives as representing mappings from properties to properties. The constructivist definition is based on an extension of Martin-L¨of's Constructive Type Theory (CTT) so as to accommodate partial verifi- cation. We show that, and why, \a is an alleged assassin" and \Allegedly, a is an assassin" are equivalent in TIL and synonymous in CTT. Keywords: Modal modification, property vs. propositional modifica- tion, alleged, allegedly, Transparent Intensional Logic, Constructive Type Theory. 1 Introduction & overview Kamp's seminal [10] seeks to draw a line between those adjectives whose mean- ing is a property and those adjectives whose meaning is a function that maps properties to properties.
    [Show full text]
  • Towards Verb Modification in Frames
    TowardsDRAFT Verb Modification in Frames A Case Study on German Schlagen (to hit) B Anja Goldschmidt1( ), Thomas Gamerschlag2, Wiebke Petersen3, Ekaterina Gabrovska2, and Wilhelm Geuder2 1 UiL OTS, Utrecht University, Utrecht, The Netherlands [email protected] 2 CRC 991, Heinrich Heine University D¨usseldorf,D¨usseldorf,Germany 3 Department of Linguistics and Information Science, Heinrich Heine University D¨usseldorf, D¨usseldorf,Germany Abstract. Hit-verbs have three basic meaning components, namely movement, contact and force (e.g. [12], Levin 1993), which interact with the verbs’ argument structure in various ways. In this paper, we map out the different grammatical constructions of the German verb schla- gen (usually, though loosely, translated as ‘hit’; also ‘beat’, ‘strike’) and their restrictions on agentivity and the force component. Using modifica- tion by pure manner adverbs as a tool to test for possible default values of the force component, and agent-oriented adverbs to discover possible interactions with agentivity, we show that German schlagen is rather lib- eral with respect to its force component. Crucially, the force component may not only be modified by standard, force-denoting manner adverbs such as lightly and hard, but also through agent-oriented adverbs such as playfully, via a defeasible inference. We show further that our findings can be profitably modelled in Frame Semantics, a framework which is especially well suited for modelling a fine-grained decomposition of word meaning, including the manner-related components of verbs. Keywords: Hit-verbs · Modification · Force · Agentivity · Frame semantics This work was funded by the Deutsche Forschungsgemeinschaft (DFG) with a grant to the Collaborative Research Centre (SFB) 991 “The Structure of Representations in Language, Cognition, and Science”, Projects B09 and C10 (Sebastian L¨obner and Wiebke Petersen).
    [Show full text]