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Author: G. Gierz
Publisher: Cambridge University Press
ISBN: 9780521803380
Category : Mathematics
Languages : en
Pages : 640
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Book Description
Table of contents
Author: G. Gierz
Publisher: Cambridge University Press
ISBN: 9780521803380
Category : Mathematics
Languages : en
Pages : 640
Get Book Here
Book Description
Table of contents
Author: G. Gierz
Publisher: Springer Science & Business Media
ISBN: 3642676782
Category : Mathematics
Languages : en
Pages : 390
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Book Description
A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.
Author: A. Jung
Publisher:
ISBN:
Category : Closed categories (Mathematics)
Languages : en
Pages : 122
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Book Description
Author: Roy L. Crole
Publisher: Cambridge University Press
ISBN: 9780521457019
Category : Computers
Languages : en
Pages : 362
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Book Description
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.
Author: Roberto Amadio
Publisher: Springer
ISBN: 3540784993
Category : Computers
Languages : en
Pages : 519
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Book Description
This book contains the proceedings of the 11th International Conference on Foundations of Software Science and Computational Structures. It covers theories and methods to support analysis, synthesis, transformation and verification of software systems.
Author: George Grätzer
Publisher: Springer
ISBN: 3319064134
Category : Mathematics
Languages : en
Pages : 472
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Book Description
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.
Author: Michael Main
Publisher: Springer Science & Business Media
ISBN: 9783540190202
Category : Mathematics
Languages : en
Pages : 652
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Book Description
This volume is the proceedings of the 3rd Workshop on the Mathematical Foundations of Programming Language Semantics held at Tulane University, New Orleans, Louisiana, April 8-10, 1987. The 1st Workshop was at Kansas State University, Manhattan, Kansas in April, 1985 (see LNCS 239), and the 2nd Workshop with a limited number of participants was at Kansas State in April, 1986. It was the intention of the organizers that the 3rd Workshop survey as many areas of the Mathematical Foundations of Programming Language Semantics as reasonably possible. The Workshop attracted 49 submitted papers, from which 28 papers were chosen for presentation. The papers ranged in subject from category theory and Lambda-calculus to the structure theory of domains and power domains, to implementation issues surrounding semantics.
Author: Guram Bezhanishvili
Publisher: Springer
ISBN: 940178860X
Category : Philosophy
Languages : en
Pages : 340
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Book Description
This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.
Author: Marco Benini
Publisher: World Scientific
ISBN: 9811245231
Category : Mathematics
Languages : en
Pages : 477
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Book Description
The overall topic of the volume, Mathematics for Computation (M4C), is mathematics taking crucially into account the aspect of computation, investigating the interaction of mathematics with computation, bridging the gap between mathematics and computation wherever desirable and possible, and otherwise explaining why not.Recently, abstract mathematics has proved to have more computational content than ever expected. Indeed, the axiomatic method, originally intended to do away with concrete computations, seems to suit surprisingly well the programs-from-proofs paradigm, with abstraction helping not only clarity but also efficiency.Unlike computational mathematics, which rather focusses on objects of computational nature such as algorithms, the scope of M4C generally encompasses all the mathematics, including abstract concepts such as functions. The purpose of M4C actually is a strongly theory-based and therefore, is a more reliable and sustainable approach to actual computation, up to the systematic development of verified software.While M4C is situated within mathematical logic and the related area of theoretical computer science, in principle it involves all branches of mathematics, especially those which prompt computational considerations. In traditional terms, the topics of M4C include proof theory, constructive mathematics, complexity theory, reverse mathematics, type theory, category theory and domain theory.The aim of this volume is to provide a point of reference by presenting up-to-date contributions by some of the most active scholars in each field. A variety of approaches and techniques are represented to give as wide a view as possible and promote cross-fertilization between different styles and traditions.
Author: M.E. Carvallo
Publisher: Springer Science & Business Media
ISBN: 9400929919
Category : Science
Languages : en
Pages : 388
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Book Description
usually called the classical (scientific) attitude (according to which there is a dichotomy between nature and cognition) and suggestions for better understanding of their mutual encroach ment. The authors belong more or less to the non-standard systems science, the third order cybernetics, or find themselves already beyond the third stage in the history of artificial intelli 1 gence ). They take the inescapability of the mutual implication of the description of nature and that of cognition seriously. Fourth ly, closely linking up with the previous, it emphatically calls attention to the forgotten microscopic dimension of science. If I am not mistaken we have at this moment reached the historic stage where the tremendous renascence of the mechanistic-structural paradigm, remarkably enough, calls for its functional-dynamic counterparts. The volume strives to respond to this secret trend in various disciplines and to put into words that which is tacitly alive in the minds of the ever increasing number of people in this systemsage. The investigation on the intertwinement of nature and cognition finds itself in this very paradoxical niche structured by those two opposite developments.
