Mathematics Colloquium: the Geometry of Syntax
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CAS LX 522 Syntax I
It is likely… CAS LX 522 IP This satisfies the EPP in Syntax I both clauses. The main DPj I′ clause has Mary in SpecIP. Mary The embedded clause has Vi+I VP is the trace in SpecIP. V AP Week 14b. PRO and control ti This specific instance of A- A IP movement, where we move a likely subject from an embedded DP I′ clause to a higher clause is tj generally called subject raising. I VP to leave Reluctance to leave Reluctance to leave Now, consider: Reluctant has two θ-roles to assign. Mary is reluctant to leave. One to the one feeling the reluctance (Experiencer) One to the proposition about which the reluctance holds (Proposition) This looks very similar to Mary is likely to leave. Can we draw the same kind of tree for it? Leave has one θ-role to assign. To the one doing the leaving (Agent). How many θ-roles does reluctant assign? In Mary is reluctant to leave, what θ-role does Mary get? IP Reluctance to leave Reluctance… DPi I′ Mary Vj+I VP In Mary is reluctant to leave, is V AP Mary is doing the leaving, gets Agent t Mary is reluctant to leave. j t from leave. i A′ Reluctant assigns its θ- Mary is showing the reluctance, gets θ roles within AP as A θ IP Experiencer from reluctant. required, Mary moves reluctant up to SpecIP in the main I′ clause by Spellout. ? And we have a problem: I vP But what gets the θ-role to Mary appears to be getting two θ-roles, from leave, and what v′ in violation of the θ-criterion. -
Germanic Standardizations: Past to Present (Impact: Studies in Language and Society)
<DOCINFO AUTHOR ""TITLE "Germanic Standardizations: Past to Present"SUBJECT "Impact 18"KEYWORDS ""SIZE HEIGHT "220"WIDTH "150"VOFFSET "4"> Germanic Standardizations Impact: Studies in language and society impact publishes monographs, collective volumes, and text books on topics in sociolinguistics. The scope of the series is broad, with special emphasis on areas such as language planning and language policies; language conflict and language death; language standards and language change; dialectology; diglossia; discourse studies; language and social identity (gender, ethnicity, class, ideology); and history and methods of sociolinguistics. General Editor Associate Editor Annick De Houwer Elizabeth Lanza University of Antwerp University of Oslo Advisory Board Ulrich Ammon William Labov Gerhard Mercator University University of Pennsylvania Jan Blommaert Joseph Lo Bianco Ghent University The Australian National University Paul Drew Peter Nelde University of York Catholic University Brussels Anna Escobar Dennis Preston University of Illinois at Urbana Michigan State University Guus Extra Jeanine Treffers-Daller Tilburg University University of the West of England Margarita Hidalgo Vic Webb San Diego State University University of Pretoria Richard A. Hudson University College London Volume 18 Germanic Standardizations: Past to Present Edited by Ana Deumert and Wim Vandenbussche Germanic Standardizations Past to Present Edited by Ana Deumert Monash University Wim Vandenbussche Vrije Universiteit Brussel/FWO-Vlaanderen John Benjamins Publishing Company Amsterdam/Philadelphia TM The paper used in this publication meets the minimum requirements 8 of American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984. Library of Congress Cataloging-in-Publication Data Germanic standardizations : past to present / edited by Ana Deumert, Wim Vandenbussche. -
Syntax and Semantics of Propositional Logic
INTRODUCTIONTOLOGIC Lecture 2 Syntax and Semantics of Propositional Logic. Dr. James Studd Logic is the beginning of wisdom. Thomas Aquinas Outline 1 Syntax vs Semantics. 2 Syntax of L1. 3 Semantics of L1. 4 Truth-table methods. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘likes logic’ is a verb phrase. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘Bertrand Russell likes logic’ is a sentence. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. ‘likes logic’ is a verb phrase. Combining a proper noun and a verb phrase in this way makes a sentence. Syntax vs. Semantics Syntax Syntax is all about expressions: words and sentences. Examples of syntactic claims ‘Bertrand Russell’ is a proper noun. -
Looking for Parametric Correlations Within Faroese Höskuldur Thráinsson University of Iceland
Looking for parametric correlations within Faroese Höskuldur Thráinsson University of Iceland Abstract: This paper first reviews some parameters that have been suggested to account for variation within Scandinavian, focussing for concreteness on the parameters proposed by Holmberg and Platzack (1995) and Bobaljik and Thráinsson (1998). As this review shows, Faroese is not as well behaved as the parametric approach to Scandinavian syntax would lead us to expect. In addition, the variation found within Faroese syntax is often gradient and not as categorical as the conventional parametric approach to variation would predict. Yet it can be shown that some of the correlations predicted by Holmberg and Platzack’s (1995) Agr Parameter and Bobaljik and Thráinsson’s (1998) Split IP Parameter are found in Faroese syntax and they are turn out to be statistically significant. In the final section it is argued that to account for facts of this sort we need to revise our ideas about parametric variation, language acquisition and the nature of internalized grammars — and that this will be necessary regardless of what we think of the particular formulation of parameters assumed by Holmberg and Platzack on the one hand and Bobaljik and Thráinsson on the other. 1. Parametric variation in Scandinavian syntax1 1.1. The agreement parameter and the case parameter In their comparative work on Scandinavian around 1990, which culminated in their influential book On the Role of Inflection in Scandinavian Syntax (1995), Holmberg and Platzack (henceforth H&P or P&H, depending on the order of authors in the relevant publications) divide the Scandinavian languages into two main groups, i.e. -
Indo-European Linguistics: an Introduction Indo-European Linguistics an Introduction
This page intentionally left blank Indo-European Linguistics The Indo-European language family comprises several hun- dred languages and dialects, including most of those spoken in Europe, and south, south-west and central Asia. Spoken by an estimated 3 billion people, it has the largest number of native speakers in the world today. This textbook provides an accessible introduction to the study of the Indo-European proto-language. It clearly sets out the methods for relating the languages to one another, presents an engaging discussion of the current debates and controversies concerning their clas- sification, and offers sample problems and suggestions for how to solve them. Complete with a comprehensive glossary, almost 100 tables in which language data and examples are clearly laid out, suggestions for further reading, discussion points and a range of exercises, this text will be an essential toolkit for all those studying historical linguistics, language typology and the Indo-European proto-language for the first time. james clackson is Senior Lecturer in the Faculty of Classics, University of Cambridge, and is Fellow and Direc- tor of Studies, Jesus College, University of Cambridge. His previous books include The Linguistic Relationship between Armenian and Greek (1994) and Indo-European Word For- mation (co-edited with Birgit Anette Olson, 2004). CAMBRIDGE TEXTBOOKS IN LINGUISTICS General editors: p. austin, j. bresnan, b. comrie, s. crain, w. dressler, c. ewen, r. lass, d. lightfoot, k. rice, i. roberts, s. romaine, n. v. smith Indo-European Linguistics An Introduction In this series: j. allwood, l.-g. anderson and o.¨ dahl Logic in Linguistics d. -
Syntax: Recursion, Conjunction, and Constituency
Syntax: Recursion, Conjunction, and Constituency Course Readings Recursion Syntax: Conjunction Recursion, Conjunction, and Constituency Tests Auxiliary Verbs Constituency . Syntax: Course Readings Recursion, Conjunction, and Constituency Course Readings Recursion Conjunction Constituency Tests The following readings have been posted to the Moodle Auxiliary Verbs course site: I Language Files: Chapter 5 (pp. 204-215, 216-220) I Language Instinct: Chapter 4 (pp. 74-99) . Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion PP ! P (NP) Conjunction CP ! C S Constituency Tests Auxiliary Verbs An Interesting Feature of These Rules: As we saw last time, these rules allow sentences to contain other sentences. I A sentence must have a VP in it. I A VP can have a CP in it. I A CP must have an S in it. Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion ! PP P (NP) Conjunction CP ! C S Constituency Tests Auxiliary Verbs An Interesting Feature of These Rules: As we saw last time, these rules allow sentences to contain other sentences. S NP VP N V CP Dave thinks C S that . he. is. cool. Syntax: An Interesting Property of our PS Rules Recursion, Conjunction, and Our Current PS Rules: Constituency S ! f NP , CP g VP NP ! (D) (A*) N (CP) (PP*) Course Readings VP ! V (NP) f (NP) (CP) g (PP*) Recursion PP ! P (NP) Conjunction CP ! CS Constituency Tests Auxiliary Verbs Another Interesting Feature of These Rules: These rules also allow noun phrases to contain other noun phrases. -
Lecture 1: Propositional Logic
Lecture 1: Propositional Logic Syntax Semantics Truth tables Implications and Equivalences Valid and Invalid arguments Normal forms Davis-Putnam Algorithm 1 Atomic propositions and logical connectives An atomic proposition is a statement or assertion that must be true or false. Examples of atomic propositions are: “5 is a prime” and “program terminates”. Propositional formulas are constructed from atomic propositions by using logical connectives. Connectives false true not and or conditional (implies) biconditional (equivalent) A typical propositional formula is The truth value of a propositional formula can be calculated from the truth values of the atomic propositions it contains. 2 Well-formed propositional formulas The well-formed formulas of propositional logic are obtained by using the construction rules below: An atomic proposition is a well-formed formula. If is a well-formed formula, then so is . If and are well-formed formulas, then so are , , , and . If is a well-formed formula, then so is . Alternatively, can use Backus-Naur Form (BNF) : formula ::= Atomic Proposition formula formula formula formula formula formula formula formula formula formula 3 Truth functions The truth of a propositional formula is a function of the truth values of the atomic propositions it contains. A truth assignment is a mapping that associates a truth value with each of the atomic propositions . Let be a truth assignment for . If we identify with false and with true, we can easily determine the truth value of under . The other logical connectives can be handled in a similar manner. Truth functions are sometimes called Boolean functions. 4 Truth tables for basic logical connectives A truth table shows whether a propositional formula is true or false for each possible truth assignment. -
1 Logic, Language and Meaning 2 Syntax and Semantics of Predicate
Semantics and Pragmatics 2 Winter 2011 University of Chicago Handout 1 1 Logic, language and meaning • A formal system is a set of primitives, some statements about the primitives (axioms), and some method of deriving further statements about the primitives from the axioms. • Predicate logic (calculus) is a formal system consisting of: 1. A syntax defining the expressions of a language. 2. A set of axioms (formulae of the language assumed to be true) 3. A set of rules of inference for deriving further formulas from the axioms. • We use this formal system as a tool for analyzing relevant aspects of the meanings of natural languages. • A formal system is a syntactic object, a set of expressions and rules of combination and derivation. However, we can talk about the relation between this system and the models that can be used to interpret it, i.e. to assign extra-linguistic entities as the meanings of expressions. • Logic is useful when it is possible to translate natural languages into a logical language, thereby learning about the properties of natural language meaning from the properties of the things that can act as meanings for a logical language. 2 Syntax and semantics of Predicate Logic 2.1 The vocabulary of Predicate Logic 1. Individual constants: fd; n; j; :::g 2. Individual variables: fx; y; z; :::g The individual variables and constants are the terms. 3. Predicate constants: fP; Q; R; :::g Each predicate has a fixed and finite number of ar- guments called its arity or valence. As we will see, this corresponds closely to argument positions for natural language predicates. -
Lambda Calculus and the Decision Problem
Lambda Calculus and the Decision Problem William Gunther November 8, 2010 Abstract In 1928, Alonzo Church formalized the λ-calculus, which was an attempt at providing a foundation for mathematics. At the heart of this system was the idea of function abstraction and application. In this talk, I will outline the early history and motivation for λ-calculus, especially in recursion theory. I will discuss the basic syntax and the primary rule: β-reduction. Then I will discuss how one would represent certain structures (numbers, pairs, boolean values) in this system. This will lead into some theorems about fixed points which will allow us have some fun and (if there is time) to supply a negative answer to Hilbert's Entscheidungsproblem: is there an effective way to give a yes or no answer to any mathematical statement. 1 History In 1928 Alonzo Church began work on his system. There were two goals of this system: to investigate the notion of 'function' and to create a powerful logical system sufficient for the foundation of mathematics. His main logical system was later (1935) found to be inconsistent by his students Stephen Kleene and J.B.Rosser, but the 'pure' system was proven consistent in 1936 with the Church-Rosser Theorem (which more details about will be discussed later). An application of λ-calculus is in the area of computability theory. There are three main notions of com- putability: Hebrand-G¨odel-Kleenerecursive functions, Turing Machines, and λ-definable functions. Church's Thesis (1935) states that λ-definable functions are exactly the functions that can be “effectively computed," in an intuitive way. -
Gender Across Languages: the Linguistic Representation of Women and Men
<DOCINFO AUTHOR "" TITLE "Gender Across Languages: The linguistic representation of women and men. Volume II" SUBJECT "Impact 10" KEYWORDS "" SIZE HEIGHT "220" WIDTH "150" VOFFSET "4"> Gender Across Languages Impact: Studies in language and society impact publishes monographs, collective volumes, and text books on topics in sociolinguistics. The scope of the series is broad, with special emphasis on areas such as language planning and language policies; language conflict and language death; language standards and language change; dialectology; diglossia; discourse studies; language and social identity (gender, ethnicity, class, ideology); and history and methods of sociolinguistics. General editor Annick De Houwer University of Antwerp Advisory board Ulrich Ammon William Labov Gerhard Mercator University University of Pennsylvania Laurie Bauer Elizabeth Lanza Victoria University of Wellington University of Oslo Jan Blommaert Joseph Lo Bianco Ghent University The Australian National University Paul Drew Peter Nelde University of York Catholic University Brussels Anna Escobar Dennis Preston University of Illinois at Urbana Michigan State University Guus Extra Jeanine Treffers-Daller Tilburg University University of the West of England Margarita Hidalgo Vic Webb San Diego State University University of Pretoria Richard A. Hudson University College London Volume 10 Gender Across Languages: The linguistic representation of women and men Volume II Edited by Marlis Hellinger and Hadumod Bußmann Gender Across Languages The linguistic representation of women and men volume 2 Edited by Marlis Hellinger University of Frankfurt am Main Hadumod Bußmann University of Munich John Benjamins Publishing Company Amsterdam/Philadelphia TM The paper used in this publication meets the minimum requirements of American 8 National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984. -
A Logical Approach to Grammar Description Lionel Clément, Jérôme Kirman, Sylvain Salvati
A logical approach to grammar description Lionel Clément, Jérôme Kirman, Sylvain Salvati To cite this version: Lionel Clément, Jérôme Kirman, Sylvain Salvati. A logical approach to grammar description. Jour- nal of Language Modelling, Institute of Computer Science, Polish Academy of Sciences, Poland, 2015, Special issue on High-level methodologies for grammar engineering, 3 (1), pp. 87-143 10.15398/jlm.v3i1.94. hal-01251222 HAL Id: hal-01251222 https://hal.archives-ouvertes.fr/hal-01251222 Submitted on 19 Jan 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A logical approach to grammar description Lionel Clément, Jérôme Kirman, and Sylvain Salvati Université de Bordeaux LaBRI France abstract In the tradition of Model Theoretic Syntax, we propose a logical ap- Keywords: proach to the description of grammars. We combine in one formal- grammar ism several tools that are used throughout computer science for their description, logic, power of abstraction: logic and lambda calculus. We propose then a Finite State high-level formalism for describing mildly context sensitive grammars Automata, and their semantic interpretation. As we rely on the correspondence logical between logic and finite state automata, our method combines con- transduction, ciseness with effectivity. -
FOL Syntax: You Will Be Expected to Know
First-Order Logic A: Syntax CS271P, Fall Quarter, 2018 Introduction to Artificial Intelligence Prof. Richard Lathrop Read Beforehand: R&N 8, 9.1-9.2, 9.5.1-9.5.5 Common Sense Reasoning Example, adapted from Lenat You are told: John drove to the grocery store and bought a pound of noodles, a pound of ground beef, and two pounds of tomatoes. • Is John 3 years old? • Is John a child? • What will John do with the purchases? • Did John have any money? • Does John have less money after going to the store? • Did John buy at least two tomatoes? • Were the tomatoes made in the supermarket? • Did John buy any meat? • Is John a vegetarian? • Will the tomatoes fit in John’s car? • Can Propositional Logic support these inferences? Outline for First-Order Logic (FOL, also called FOPC) • Propositional Logic is Useful --- but Limited Expressive Power • First Order Predicate Calculus (FOPC), or First Order Logic (FOL). – FOPC has expanded expressive power, though still limited. • New Ontology – The world consists of OBJECTS. – OBJECTS have PROPERTIES, RELATIONS, and FUNCTIONS. • New Syntax – Constants, Predicates, Functions, Properties, Quantifiers. • New Semantics – Meaning of new syntax. • Unification and Inference in FOL • Knowledge engineering in FOL FOL Syntax: You will be expected to know • FOPC syntax – Syntax: Sentences, predicate symbols, function symbols, constant symbols, variables, quantifiers • De Morgan’s rules for quantifiers – connections between ∀ and ∃ • Nested quantifiers – Difference between “∀ x ∃ y P(x, y)” and “∃ x ∀ y P(x, y)”