Download or read book Finite Model Theory and Its Applications written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.
Download or read book Introduction to Model Theory written by Philipp Rothmaler and published by CRC Press. This book was released on 2018-12-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Model Theory and Applications written by O.V. Belegradek and published by American Mathematical Soc.. This book was released on 1999 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.
Download or read book Model Theory An Introduction written by David Marker and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Download or read book Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1993-03-11 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.
Download or read book An Invitation to Model Theory written by Jonathan Kirby and published by Cambridge University Press. This book was released on 2019-04-18 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.
Download or read book Mathematical Logic and Model Theory written by Alexander Prestel and published by Springer Science & Business Media. This book was released on 2011-08-21 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Download or read book A Functorial Model Theory written by Cyrus F. Nourani and published by CRC Press. This book was released on 2016-04-19 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Download or read book Mixed Models written by Eugene Demidenko and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition “This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one’s personal library.” —Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal data, modeling data with multiple sources of variation, modeling biological variety and heterogeneity, Healthy Akaike Information Criterion (HAIC), parameter multidimensionality, and statistics of image processing. Mixed Models: Theory and Applications with R, Second Edition features unique applications of mixed model methodology, as well as: Comprehensive theoretical discussions illustrated by examples and figures Over 300 exercises, end-of-section problems, updated data sets, and R subroutines Problems and extended projects requiring simulations in R intended to reinforce material Summaries of major results and general points of discussion at the end of each chapter Open problems in mixed modeling methodology, which can be used as the basis for research or PhD dissertations Ideal for graduate-level courses in mixed statistical modeling, the book is also an excellent reference for professionals in a range of fields, including cancer research, computer science, and engineering.
Download or read book A Shorter Model Theory written by Wilfrid Hodges and published by Cambridge University Press. This book was released on 1997-04-10 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Download or read book Mixed Models written by Eugene Demidenko and published by John Wiley & Sons. This book was released on 2005-01-28 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous, self-contained examination of mixed model theory and application Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. Paying special attention to algorithms and their implementations, the book discusses: Modeling of complex clustered or longitudinal data Modeling data with multiple sources of variation Modeling biological variety and heterogeneity Mixed model as a compromise between the frequentist and Bayesian approaches Mixed model for the penalized log-likelihood Healthy Akaike Information Criterion (HAIC) How to cope with parameter multidimensionality How to solve ill-posed problems including image reconstruction problems Modeling of ensemble shapes and images Statistics of image processing Major results and points of discussion at the end of each chapter along with "Summary Points" sections make this reference not only comprehensive but also highly accessible for professionals and students alike in a broad range of fields such as cancer research, computer science, engineering, and industry.
Download or read book Model Theory and Algebraic Geometry written by Elisabeth Bouscaren and published by Springer. This book was released on 2009-03-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Download or read book Elements of Finite Model Theory written by Leonid Libkin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.
Download or read book Systems Engineering Models written by Adedeji B. Badiru and published by CRC Press. This book was released on 2019-03-19 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive compilation of practical systems engineering models. The application and recognition of systems engineering is spreading rapidly, however there is no book that addresses the availability and usability of systems engineering models. Notable among the models to be included are the V-Model, DEJI Model, and Waterfall Model. There are other models developed for specific organizational needs, which will be identified and presented in a practical template so that other organizations can learn and use them. A better understanding of the models, through a comprehensive book, will make these models more visible, embraced, and applied across the spectrum. Visit www.DEJImodel.com for model details. Features Covers applications to both small and large problems Displays decomposition of complex problems into smaller manageable chunks Discusses direct considerations of the pertinent constraints that exist in the problem domain Presents systematic linking of inputs to goals and outputs
Download or read book A Course in Model Theory written by Bruno Poizat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
Download or read book Model Theory for Beginners 15 Lectures written by Roman Kossak and published by . This book was released on 2021-02-10 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
