Topoi
Topoi

Author: R. Goldblatt

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 569

ISBN-13: 148329921X

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The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

An Introduction to Categorical Data Analysis
An Introduction to Categorical Data Analysis

Author: Alan Agresti

Publisher: John Wiley & Sons

Published: 2018-10-11

Total Pages: 393

ISBN-13: 1119405270

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A valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: • Illustrations of the use of R software to perform all the analyses in the book • A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis • New sections in many chapters introducing the Bayesian approach for the methods of that chapter • More than 70 analyses of data sets to illustrate application of the methods, and about 200 exercises, many containing other data sets • An appendix showing how to use SAS, Stata, and SPSS, and an appendix with short solutions to most odd-numbered exercises Written in an applied, nontechnical style, this book illustrates the methods using a wide variety of real data, including medical clinical trials, environmental questions, drug use by teenagers, horseshoe crab mating, basketball shooting, correlates of happiness, and much more. An Introduction to Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and biostatisticians as well as methodologists in the social and behavioral sciences, medicine and public health, marketing, education, and the biological and agricultural sciences.

Categorical Data Analysis
Categorical Data Analysis

Author: Alan Agresti

Publisher: John Wiley & Sons

Published: 2013-04-08

Total Pages: 756

ISBN-13: 1118710940

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Praise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis." —Statistics in Medicine "It is a total delight reading this book." —Pharmaceutical Research "If you do any analysis of categorical data, this is an essential desktop reference." —Technometrics The use of statistical methods for analyzing categorical data has increased dramatically, particularly in the biomedical, social sciences, and financial industries. Responding to new developments, this book offers a comprehensive treatment of the most important methods for categorical data analysis. Categorical Data Analysis, Third Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial loglinear models for discrete data with normal regression for continuous data. This edition also features: An emphasis on logistic and probit regression methods for binary, ordinal, and nominal responses for independent observations and for clustered data with marginal models and random effects models Two new chapters on alternative methods for binary response data, including smoothing and regularization methods, classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections introducing the Bayesian approach for methods in that chapter More than 100 analyses of data sets and over 600 exercises Notes at the end of each chapter that provide references to recent research and topics not covered in the text, linked to a bibliography of more than 1,200 sources A supplementary website showing how to use R and SAS; for all examples in the text, with information also about SPSS and Stata and with exercise solutions Categorical Data Analysis, Third Edition is an invaluable tool for statisticians and methodologists, such as biostatisticians and researchers in the social and behavioral sciences, medicine and public health, marketing, education, finance, biological and agricultural sciences, and industrial quality control.

Categorial Morphology (RLE Linguistics B: Grammar)
Categorial Morphology (RLE Linguistics B: Grammar)

Author: Jack Hoeksema

Publisher: Routledge

Published: 2014-02-03

Total Pages: 249

ISBN-13: 1317933745

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This book presents an account of certain problems of morphological analysis that occurs within a theoretical framework that derives its inspiration from recent studies of the lexicon in generative grammar. The starting point is the controversy about the proper analysis of synthetic compounds. Are they really compounds, or phrasal derivations, or do they constitute a type of word formation of their own?

Syntax - Theory and Analysis. Volume 2
Syntax - Theory and Analysis. Volume 2

Author: Tibor Kiss

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2015-02-24

Total Pages: 726

ISBN-13: 3110393166

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This Handbook represents the development of research and the current level of knowledge in the fields of syntactic theory and syntax analysis. Syntax can look back to a long tradition. Especially in the last 50 years, however, the interaction between syntactic theory and syntactic analysis has led to a rapid increase in analyses and theoretical suggestions. This second edition of the Handbook on Syntax adopts a unifying perspective and therefore does not place the division of syntactic theory into several schools to the fore, but the increase in knowledge resulting from the fruitful argumentations between syntactic analysis and syntactic theory. It uses selected phenomena of individual languages and their cross-linguistic realizations to explain what syntactic analyses can do and at the same time to show in what respects syntactic theories differ from each other. It investigates how syntax is related to neighbouring disciplines and investigate the role of the interfaces especially the relationship between syntax and phonology, morphology, compositional semantics, pragmatics, and the lexicon. The phenomena chosen bring together renowned experts in syntax, and represent the consensus reached as to what has to be considered as an important as well as illustrative syntactic phenomenon. The phenomena discuss do not only serve to show syntactic analyses, but also to compare theoretical approaches with each other.

Categorical Variables in Developmental Research
Categorical Variables in Developmental Research

Author: Alexander von Eye

Publisher: Elsevier

Published: 1996-02-05

Total Pages: 307

ISBN-13: 0080528716

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Categorical Variables in Developmental Research provides developmental researchers with the basic tools for understanding how to utilize categorical variables in their data analysis. Covering the measurement of individual differences in growth rates, the measurement of stage transitions, latent class and log-linear models, chi-square, and more, the book provides a means for developmental researchers to make use of categorical data. - Measurement and repeated observations of categorical data - Catastrophe theory - Latent class and log-linear models - Applications

Graphical Data Analysis with R
Graphical Data Analysis with R

Author: Antony Unwin

Publisher: CRC Press

Published: 2015-03-25

Total Pages: 306

ISBN-13: 1498715249

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See How Graphics Reveal Information Graphical Data Analysis with R shows you what information you can gain from graphical displays. The book focuses on why you draw graphics to display data and which graphics to draw (and uses R to do so). All the datasets are available in R or one of its packages and the R code is available at rosuda.org/GDA. Graphical data analysis is useful for data cleaning, exploring data structure, detecting outliers and unusual groups, identifying trends and clusters, spotting local patterns, evaluating modelling output, and presenting results. This book guides you in choosing graphics and understanding what information you can glean from them. It can be used as a primary text in a graphical data analysis course or as a supplement in a statistics course. Colour graphics are used throughout.

Theory of Questions
Theory of Questions

Author: Anna Brożek

Publisher: Rodopi

Published: 2015-06-29

Total Pages: 422

ISBN-13: 9401207321

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Preliminary material /Editors Theory of Questions -- INTRODUCTION /Editors Theory of Questions -- ONTOLOGICAL AND EPISTEMOLOGICAL PRELIMINARIES /Editors Theory of Questions -- SEMANTICS AND PRAGMATICS /Editors Theory of Questions -- SENTENCES AND PICTURES OF SITUATIONS /Editors Theory of Questions -- SEMANTICO-CATEGORIAL ANALYSIS /Editors Theory of Questions -- THE COMMUNICATIVE FUNCTION OF QUESTIONS /Editors Theory of Questions -- THE STRUCTURE OF NATURAL-LANGUAGE QUESTIONS /Editors Theory of Questions -- SEMANTICO-CATEGORIAL DESCRIPTION OF QUESTIONS /Editors Theory of Questions -- COGNITIVE CONTENT AND COGNITIVE CONTEXT OF QUESTIONS /Editors Theory of Questions -- ANSWERS /Editors Theory of Questions -- EMBEDDED QUESTIONS /Editors Theory of Questions -- THE ANALYSIS OF EROTETIC SITUATION /Editors Theory of Questions -- QUESTIONS IN SCIENCE /Editors Theory of Questions -- EROTETIC REASONING /Editors Theory of Questions -- PSYCHOLOGICAL ANALYSIS OF QUESTIONS /Editors Theory of Questions -- QUESTIONS IN SURVEYS /Editors Theory of Questions -- QUESTIONS IN DIDACTIC TESTS /Editors Theory of Questions -- QUESTIONS IN LEGAL PROCEEDINGS /Editors Theory of Questions -- PHILOSOPHICAL QUESTIONS /Editors Theory of Questions -- CONCLUSIONS /Editors Theory of Questions -- FROM THE HISTORY OF EROTETICS IN POLAND IN THE 20TH CENTURY144 /Editors Theory of Questions -- REFERENCES /Editors Theory of Questions -- NAME INDEX /Editors Theory of Questions.

Human Nature
Human Nature

Author: P. M. S. Hacker

Publisher: John Wiley & Sons

Published: 2011-07-22

Total Pages: 340

ISBN-13: 1444351516

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This major new study by one of the most penetrating and persistent critics of philosophical and scientific orthodoxy, returns to Aristotle in order to examine the salient categories in terms of which we think about ourselves and our nature, and the distinctive forms of explanation we invoke to render ourselves intelligible to ourselves. The culmination of 40 years of thought on the philosophy of mind and the nature of the mankind Written by one of the world’s leading philosophers, the co-author of the monumental 4 volume Analytical Commentary on the Philosophical Investigations (Blackwell Publishing, 1980-2004) Uses broad categories, such as substance, causation, agency and power to examine how we think about ourselves and our nature Platonic and Aristotelian conceptions of human nature are sketched and contrasted Individual chapters clarify and provide an historical overview of a specific concept, then link the concept to ideas contained in other chapters

Categories for Types
Categories for Types

Author: Roy L. Crole

Publisher: Cambridge University Press

Published: 1993

Total Pages: 362

ISBN-13: 9780521457019

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This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.