Topological Duality for Distributive Lattices

Topological Duality for Distributive Lattices
Author: Mai Gehrke
Publisher: Cambridge University Press
Total Pages: 369
Release: 2024-02-29
Genre: Computers
ISBN: 1009349694

Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.

Hiroakira Ono on Substructural Logics

Hiroakira Ono on Substructural Logics
Author: Nikolaos Galatos
Publisher: Springer Nature
Total Pages: 382
Release: 2021-12-13
Genre: Philosophy
ISBN: 3030769208

This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.

Duality and Definability in First Order Logic

Duality and Definability in First Order Logic
Author: Michael Makkai
Publisher: American Mathematical Soc.
Total Pages: 122
Release: 1993
Genre: Mathematics
ISBN: 0821825658

We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a conservative pretopos morphism between Boolean pretoposes is canonically equivalent to the domain-pretopos. The descent theorem contains the Beth definability theorem for classical first order logic. Moreover, it gives, via the standard translation from the language of categories to symbolic logic, a new definability theorem for classical first order logic concerning set-valued functors on models, expressible in purely syntactical (arithmetical) terms.

Mathematics, Logic, and their Philosophies

Mathematics, Logic, and their Philosophies
Author: Mojtaba Mojtahedi
Publisher: Springer Nature
Total Pages: 493
Release: 2021-02-09
Genre: Philosophy
ISBN: 3030536548

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

General Lattice Theory

General Lattice Theory
Author: George Grätzer
Publisher: Springer Science & Business Media
Total Pages: 688
Release: 2002-11-21
Genre: Mathematics
ISBN: 9783764369965

"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS

Logic, Language, Information and Computation

Logic, Language, Information and Computation
Author: Hiroakira Ono
Publisher: Springer
Total Pages: 418
Release: 2009-06-07
Genre: Computers
ISBN: 3642022618

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 4th volume of the FoLLI LNAI subline; containing the refereed proceedings of the 16h International Workshop on Logic, Language, Information and Computation, WoLLIC 2009, held in Tokyo, Japan, in June 2009. The 25 revised full papers presented together with six tutorials and invited talks were carefully reviewed and selected from 57 submissions. The papers cover some of the most active areas of research on the frontiers between computation, logic, and linguistics, with particular interest in cross-disciplinary topics. Typical areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection.

Orders: Description and Roles

Orders: Description and Roles
Author: M. Pouzet
Publisher: Elsevier
Total Pages: 599
Release: 1984-01-01
Genre: Mathematics
ISBN: 0080872107

Orders: Description and Roles

From Sets and Types to Topology and Analysis

From Sets and Types to Topology and Analysis
Author: Laura Crosilla
Publisher: Oxford University Press
Total Pages: 371
Release: 2005-10-06
Genre: Mathematics
ISBN: 0198566514

Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.