Lecture 2: Formal Semantics in Logic and Linguistics
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Acquaintance Inferences As Evidential Effects
The acquaintance inference as an evidential effect Abstract. Predications containing a special restricted class of predicates, like English tasty, tend to trigger an inference when asserted, to the effect that the speaker has had a spe- cific kind of `direct contact' with the subject of predication. This `acquaintance inference' has typically been treated as a hard-coded default effect, derived from the nature of the predicate together with the commitments incurred by assertion. This paper reevaluates the nature of this inference by examining its behavior in `Standard' Tibetan, a language that grammatically encodes perceptual evidentiality. In Tibetan, the acquaintance inference trig- gers not as a default, but rather when, and only when, marked by a perceptual evidential. The acquaintance inference is thus a grammaticized evidential effect in Tibetan, and so it cannot be a default effect in general cross-linguistically. An account is provided of how the semantics of the predicate and the commitment to perceptual evidentiality derive the in- ference in Tibetan, and it is suggested that the inference ought to be seen as an evidential effect generally, even in evidential-less languages, which invoke evidential notions without grammaticizing them. 1 Introduction: the acquaintance inference A certain restricted class of predicates, like English tasty, exhibit a special sort of behavior when used in predicative assertions. In particular, they require as a robust default that the speaker of the assertion has had direct contact of a specific sort with the subject of predication, as in (1). (1) This food is tasty. ,! The speaker has tasted the food. ,! The speaker liked the food's taste. -
Compositional and Lexical Semantics • Compositional Semantics: The
Compositional and lexical semantics Compositional semantics: the construction • of meaning (generally expressed as logic) based on syntax. This lecture: – Semantics with FS grammars Lexical semantics: the meaning of • individual words. This lecture: – lexical semantic relations and WordNet – one technique for word sense disambiguation 1 Simple compositional semantics in feature structures Semantics is built up along with syntax • Subcategorization `slot' filling instantiates • syntax Formally equivalent to logical • representations (below: predicate calculus with no quantifiers) Alternative FS encodings possible • 2 Objective: obtain the following semantics for they like fish: pron(x) (like v(x; y) fish n(y)) ^ ^ Feature structure encoding: 2 PRED and 3 6 7 6 7 6 7 6 2 PRED 3 7 6 pron 7 6 ARG1 7 6 6 7 7 6 6 ARG1 1 7 7 6 6 7 7 6 6 7 7 6 6 7 7 6 4 5 7 6 7 6 7 6 2 3 7 6 PRED and 7 6 7 6 6 7 7 6 6 7 7 6 6 7 7 6 6 2 3 7 7 6 6 PRED like v 7 7 6 6 7 7 6 6 6 7 7 7 6 6 ARG1 6 ARG1 1 7 7 7 6 6 6 7 7 7 6 6 6 7 7 7 6 6 6 7 7 7 6 ARG2 6 6 ARG2 2 7 7 7 6 6 6 7 7 7 6 6 6 7 7 7 6 6 6 7 7 7 6 6 4 5 7 7 6 6 7 7 6 6 7 7 6 6 2 3 7 7 6 6 PRED fish n 7 7 6 6 ARG2 7 7 6 6 6 7 7 7 6 6 6 ARG 2 7 7 7 6 6 6 1 7 7 7 6 6 6 7 7 7 6 6 6 7 7 7 6 6 4 5 7 7 6 6 7 7 6 4 5 7 6 7 4 5 3 Noun entry 2 3 2 CAT noun 3 6 HEAD 7 6 7 6 6 AGR 7 7 6 6 7 7 6 6 7 7 6 4 5 7 6 7 6 COMP 7 6 filled 7 6 7 fish 6 7 6 SPR filled 7 6 7 6 7 6 7 6 INDEX 1 7 6 2 3 7 6 7 6 SEM 7 6 6 PRED fish n 7 7 6 6 7 7 6 6 7 7 6 6 ARG 1 7 7 6 6 1 7 7 6 6 7 7 6 6 7 7 6 4 5 7 4 5 Corresponds to fish(x) where the INDEX • points to the characteristic variable of the noun (that is x). -
Data Types & Arithmetic Expressions
Data Types & Arithmetic Expressions 1. Objective .............................................................. 2 2. Data Types ........................................................... 2 3. Integers ................................................................ 3 4. Real numbers ....................................................... 3 5. Characters and strings .......................................... 5 6. Basic Data Types Sizes: In Class ......................... 7 7. Constant Variables ............................................... 9 8. Questions/Practice ............................................. 11 9. Input Statement .................................................. 12 10. Arithmetic Expressions .................................... 16 11. Questions/Practice ........................................... 21 12. Shorthand operators ......................................... 22 13. Questions/Practice ........................................... 26 14. Type conversions ............................................. 28 Abdelghani Bellaachia, CSCI 1121 Page: 1 1. Objective To be able to list, describe, and use the C basic data types. To be able to create and use variables and constants. To be able to use simple input and output statements. Learn about type conversion. 2. Data Types A type defines by the following: o A set of values o A set of operations C offers three basic data types: o Integers defined with the keyword int o Characters defined with the keyword char o Real or floating point numbers defined with the keywords -
Sentential Negation and Negative Concord
Sentential Negation and Negative Concord Published by LOT phone: +31.30.2536006 Trans 10 fax: +31.30.2536000 3512 JK Utrecht email: [email protected] The Netherlands http://wwwlot.let.uu.nl/ Cover illustration: Kasimir Malevitch: Black Square. State Hermitage Museum, St. Petersburg, Russia. ISBN 90-76864-68-3 NUR 632 Copyright © 2004 by Hedde Zeijlstra. All rights reserved. Sentential Negation and Negative Concord ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus Prof. Mr P.F. van der Heijden ten overstaan van een door het College voor Promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op woensdag 15 december 2004, te 10:00 uur door HEDZER HUGO ZEIJLSTRA geboren te Rotterdam Promotiecommissie: Promotores: Prof. Dr H.J. Bennis Prof. Dr J.A.G. Groenendijk Copromotor: Dr J.B. den Besten Leden: Dr L.C.J. Barbiers (Meertens Instituut, Amsterdam) Dr P.J.E. Dekker Prof. Dr A.C.J. Hulk Prof. Dr A. von Stechow (Eberhard Karls Universität Tübingen) Prof. Dr F.P. Weerman Faculteit der Geesteswetenschappen Voor Petra Table of Contents TABLE OF CONTENTS ............................................................................................ I ACKNOWLEDGEMENTS .......................................................................................V 1 INTRODUCTION................................................................................................1 1.1 FOUR ISSUES IN THE STUDY OF NEGATION.......................................................1 -
Chapter 1 Negation in a Cross-Linguistic Perspective
Chapter 1 Negation in a cross-linguistic perspective 0. Chapter summary This chapter introduces the empirical scope of our study on the expression and interpretation of negation in natural language. We start with some background notions on negation in logic and language, and continue with a discussion of more linguistic issues concerning negation at the syntax-semantics interface. We zoom in on cross- linguistic variation, both in a synchronic perspective (typology) and in a diachronic perspective (language change). Besides expressions of propositional negation, this book analyzes the form and interpretation of indefinites in the scope of negation. This raises the issue of negative polarity and its relation to negative concord. We present the main facts, criteria, and proposals developed in the literature on this topic. The chapter closes with an overview of the book. We use Optimality Theory to account for the syntax and semantics of negation in a cross-linguistic perspective. This theoretical framework is introduced in Chapter 2. 1 Negation in logic and language The main aim of this book is to provide an account of the patterns of negation we find in natural language. The expression and interpretation of negation in natural language has long fascinated philosophers, logicians, and linguists. Horn’s (1989) Natural history of negation opens with the following statement: “All human systems of communication contain a representation of negation. No animal communication system includes negative utterances, and consequently, none possesses a means for assigning truth value, for lying, for irony, or for coping with false or contradictory statements.” A bit further on the first page, Horn states: “Despite the simplicity of the one-place connective of propositional logic ( ¬p is true if and only if p is not true) and of the laws of inference in which it participate (e.g. -
Calculus Terminology
AP Calculus BC Calculus Terminology Absolute Convergence Asymptote Continued Sum Absolute Maximum Average Rate of Change Continuous Function Absolute Minimum Average Value of a Function Continuously Differentiable Function Absolutely Convergent Axis of Rotation Converge Acceleration Boundary Value Problem Converge Absolutely Alternating Series Bounded Function Converge Conditionally Alternating Series Remainder Bounded Sequence Convergence Tests Alternating Series Test Bounds of Integration Convergent Sequence Analytic Methods Calculus Convergent Series Annulus Cartesian Form Critical Number Antiderivative of a Function Cavalieri’s Principle Critical Point Approximation by Differentials Center of Mass Formula Critical Value Arc Length of a Curve Centroid Curly d Area below a Curve Chain Rule Curve Area between Curves Comparison Test Curve Sketching Area of an Ellipse Concave Cusp Area of a Parabolic Segment Concave Down Cylindrical Shell Method Area under a Curve Concave Up Decreasing Function Area Using Parametric Equations Conditional Convergence Definite Integral Area Using Polar Coordinates Constant Term Definite Integral Rules Degenerate Divergent Series Function Operations Del Operator e Fundamental Theorem of Calculus Deleted Neighborhood Ellipsoid GLB Derivative End Behavior Global Maximum Derivative of a Power Series Essential Discontinuity Global Minimum Derivative Rules Explicit Differentiation Golden Spiral Difference Quotient Explicit Function Graphic Methods Differentiable Exponential Decay Greatest Lower Bound Differential -
Parsing Arithmetic Expressions Outline
Parsing Arithmetic Expressions https://courses.missouristate.edu/anthonyclark/333/ Outline Topics and Learning Objectives • Learn about parsing arithmetic expressions • Learn how to handle associativity with a grammar • Learn how to handle precedence with a grammar Assessments • ANTLR grammar for math Parsing Expressions There are a variety of special purpose algorithms to make this task more efficient: • The shunting yard algorithm https://eli.thegreenplace.net/2010/01/02 • Precedence climbing /top-down-operator-precedence-parsing • Pratt parsing For this class we are just going to use recursive descent • Simpler • Same as the rest of our parser Grammar for Expressions Needs to account for operator associativity • Also known as fixity • Determines how you apply operators of the same precedence • Operators can be left-associative or right-associative Needs to account for operator precedence • Precedence is a concept that you know from mathematics • Think PEMDAS • Apply higher precedence operators first Associativity By convention 7 + 3 + 1 is equivalent to (7 + 3) + 1, 7 - 3 - 1 is equivalent to (7 - 3) – 1, and 12 / 3 * 4 is equivalent to (12 / 3) * 4 • If we treated 7 - 3 - 1 as 7 - (3 - 1) the result would be 5 instead of the 3. • Another way to state this convention is associativity Associativity Addition, subtraction, multiplication, and division are left-associative - What does this mean? You have: 1 - 2 - 3 - 3 • operators (+, -, *, /, etc.) and • operands (numbers, ids, etc.) 1 2 • Left-associativity: if an operand has operators -
Arithmetic Expression Construction
1 Arithmetic Expression Construction 2 Leo Alcock Sualeh Asif Harvard University, Cambridge, MA, USA MIT, Cambridge, MA, USA 3 Jeffrey Bosboom Josh Brunner MIT CSAIL, Cambridge, MA, USA MIT CSAIL, Cambridge, MA, USA 4 Charlotte Chen Erik D. Demaine MIT, Cambridge, MA, USA MIT CSAIL, Cambridge, MA, USA 5 Rogers Epstein Adam Hesterberg MIT CSAIL, Cambridge, MA, USA Harvard University, Cambridge, MA, USA 6 Lior Hirschfeld William Hu MIT, Cambridge, MA, USA MIT, Cambridge, MA, USA 7 Jayson Lynch Sarah Scheffler MIT CSAIL, Cambridge, MA, USA Boston University, Boston, MA, USA 8 Lillian Zhang 9 MIT, Cambridge, MA, USA 10 Abstract 11 When can n given numbers be combined using arithmetic operators from a given subset of 12 {+, −, ×, ÷} to obtain a given target number? We study three variations of this problem of 13 Arithmetic Expression Construction: when the expression (1) is unconstrained; (2) has a specified 14 pattern of parentheses and operators (and only the numbers need to be assigned to blanks); or 15 (3) must match a specified ordering of the numbers (but the operators and parenthesization are 16 free). For each of these variants, and many of the subsets of {+, −, ×, ÷}, we prove the problem 17 NP-complete, sometimes in the weak sense and sometimes in the strong sense. Most of these proofs 18 make use of a rational function framework which proves equivalence of these problems for values in 19 rational functions with values in positive integers. 20 2012 ACM Subject Classification Theory of computation → Problems, reductions and completeness 21 Keywords and phrases Hardness, algebraic complexity, expression trees 22 Digital Object Identifier 10.4230/LIPIcs.ISAAC.2020.41 23 Related Version A full version of the paper is available on arXiv. -
The Logic of Argument Structure
32 San Diego Linguistic Papers 3 (2008) 32-125 Circumstances and Perspective: The Logic of Argument Structure Jean Mark Gawron San Diego State University 1 Introduction The fox knows many things but the hedgehog knows one big thing. Archilochus cited by Isaiah Berlin Berlin (1997:“The Hedgehog and the Fox”) The last couple of decades have seen substantial progress in the study of lexical semantics, particularly in contributing to the understanding of how lexical semantic properties interact with syntactic properties, but many open questions await resolution before a consensus of what a theory of lexical semantics looks like is achieved. Two properties of word meanings contribute to the difficulty of the problem. One is the openness of word meanings. The variety of word meanings is the variety of human experience. Consider defining words such as ricochet, barber, alimony, seminal, amputate, and brittle. One needs to make reference to diverse practices, processes, and objects in the social and physical world: the impingement of one object against another, grooming and hair, marriage and divorce, discourse about concepts and theories, and events of breaking. Before this seemingly endless diversity, semanticists have in the past stopped short, excluding it from the semantic enterprise, and attempting to draw a line between a small linguistically significant set of concepts and the openness of the lexicon. The other problem is the closely related problem of the richness of word meanings. Words are hard to define, not so much because they invoke fine content specific distinctions, but because they invoke vast amounts of background information. The concept of buying presupposes the complex social fact of a commercial event. -
Grounding Lexical Meaning in Core Cognition
Grounding Lexical Meaning in Core Cognition Noah D. Goodman December 2012 (Updated June 2013) Abstract Author's note: This document is a slightly updated and reformatted extract from a grant proposal to the ONR. As a proposal, it aims describe useful directions while reviewing existing and pilot work; it has no pretensions to being a systematic, rigorous, or entirely coherent scholarly work. On the other hand, I've found that it provides a useful overview of a few ideas on the architecture of natural language that haven't yet appeared elsewhere. I provide it for those interested, but with all due caveats. Words are potentially one of the clearest windows on human knowledge and con- ceptual structure. But what do words mean? In this project we aim to construct and explore a formal model of lexical semantics grounded, via pragmatic inference, in core conceptual structures. Flexible human cognition is derived in large part from our ability to imagine possible worlds. A rich set of concepts, in- tuitive theories, and other mental representations support imagining and reasoning about possible worlds|together we call these core cognition. Here we posit that the collection of core concepts also forms the set of primitive elements available for lexi- cal semantics: word meanings are built from pieces of core cognition. We propose to study lexical semantics in the setting of an architecture for language understanding that integrates literal meaning with pragmatic inference. This architecture supports underspecified and uncertain lexical meaning, leading to subtle interactions between meaning, conceptual structure, and context. We will explore several cases of lexical semantics where these interactions are particularly important: indexicals, scalar adjec- tives, generics, and modals. -
Contradiction Detection with Contradiction-Specific Word Embedding
algorithms Article Contradiction Detection with Contradiction-Specific Word Embedding Luyang Li, Bing Qin * and Ting Liu Research Center for Social Computing and Information Retrieval, School of Computer Science and Technology, Harbin Institute of Technology, Haerbin 150001, China; [email protected] (L.L.); [email protected] (T.L.) * Correspondence: [email protected]; Tel.: +86-186-8674-8930 Academic Editor: Toly Chen Received: 18 January 2017; Accepted: 12 May 2017; Published: 24 May 2017 Abstract: Contradiction detection is a task to recognize contradiction relations between a pair of sentences. Despite the effectiveness of traditional context-based word embedding learning algorithms in many natural language processing tasks, such algorithms are not powerful enough for contradiction detection. Contrasting words such as “overfull” and “empty” are mostly mapped into close vectors in such embedding space. To solve this problem, we develop a tailored neural network to learn contradiction-specific word embedding (CWE). The method can separate antonyms in the opposite ends of a spectrum. CWE is learned from a training corpus which is automatically generated from the paraphrase database, and is naturally applied as features to carry out contradiction detection in SemEval 2014 benchmark dataset. Experimental results show that CWE outperforms traditional context-based word embedding in contradiction detection. The proposed model for contradiction detection performs comparably with the top-performing system in accuracy of three-category classification and enhances the accuracy from 75.97% to 82.08% in the contradiction category. Keywords: contradiction detection; word embedding; training data generation; neural network 1. Introduction Contradiction is a kind of semantic relation between sentences. -
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.