Download or read book Duality and Definability in First Order Logic written by Michael Makkai and published by American Mathematical Soc.. This book was released on 1993 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Heyting Algebras written by Leo Esakia and published by Springer. This book was released on 2019-07-05 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia spaces. The main theorems include a duality between the categories of closure algebras and of hybrids, and a duality between the categories of Heyting algebras and of so-called strict hybrids. Esakia’s book was originally published in 1985. It was the first of a planned two-volume monograph on Heyting algebras. But after the collapse of the Soviet Union, the publishing house closed and the project died with it. Fortunately, this important work now lives on in this accessible translation. The Appendix of the book discusses the planned contents of the lost second volume.

Download or read book Duality in 19th and 20th Century Mathematical Thinking written by Ralf Krömer and published by Springer Nature. This book was released on 2024 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.

Download or read book Leo Esakia on Duality in Modal and Intuitionistic Logics written by Guram Bezhanishvili and published by Springer. This book was released on 2014-06-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Topological Duality for Distributive Lattices written by Mai Gehrke and published by Cambridge University Press. This book was released on 2024-02-29 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Theory of the Knowledge Square The Fuzzy Rational Foundations of the Knowledge Production Systems written by Kofi Kissi Dompere and published by Springer. This book was released on 2012-08-28 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph is about a meta-theory of knowledge-production process and the logical pathway that connects the epistemic possibility to the epistemic reality. It examines the general conditions of paradigms for information processing and isolates the classical and fuzzy paradigms for comparative analysis. The sets of conditions that give rise to them are defined, stated and analyzed to abstract the corresponding sets of laws of thought. The fuzzy paradigm with its corresponding logic and mathematics is related to inexact symbolism for the defective information structure where the results of the knowledge production must satisfy the epistemic conditionality, composed of fuzzy conditionality and fuzzy-stochastic conditionality under the principle of logical duality with continuum. The classical paradigm with its corresponding logic and mathematics is related to exact symbolism for exact information structure where the vagueness component of the defectiveness is assumed away, and where the results of the knowledge production must satisfy no epistemic conditionality or at the maximum only the stochastic conditionality under the principle of logical dualism with excluded middle. It is argued that the epistemic path that links ontological space to the epistemological space is information. The ontological space is taken as the primary category of reality while the epistemological space is shone to be a derivative. Such information is universally defective and together with assumptions imposed guides the development of paradigms with their laws of thought, logic of reasoning, mathematics and computational techniques. The relational structure is seen in terms of logical trinity with a given example as matter-information-energy transformational trinity which is supported by the time trinity of past-present-future relationality. The book is written for professionals, researchers and students working in philosophy of science, decision-choice theories, economies, sciences, computer science, engineering, cognitive psychology and researchers working on, or interested in fuzzy paradigm, fuzzy logic, fuzzy decisions, and phenomena of vagueness and ambiguities, fuzzy mathematics, fuzzy-stochastic processes and theory of knowledge. It is further aimed at research institutions and libraries. The subject matter belongs to extensive research and development taking place on fuzzy phenomena and the debate between the fuzzy paradigm and the classical paradigm relative to informatics, synergetic science and complexity theory. The book will have a global appeal and across disciplines. Its strength, besides the contents, is the special effort that is undertaken to make it relevant and accessible to different areas of sciences and knowledge production.

Download or read book Advances in Global Optimization written by David Gao and published by Springer. This book was released on 2014-11-11 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.

Download or read book Algebra Mathematical Logic Number Theory Topology written by Ivan Matveevich Vinogradov and published by American Mathematical Soc.. This book was released on 1986 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of papers on the current research in algebra, mathematical logic, number theory and topology.

Download or read book Quantifiers Questions and Quantum Physics written by Daniel Kolak and published by Springer Science & Business Media. This book was released on 2007-11-10 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jaakko Hintikka is one of the most creative figures in contemporary philosophy. He has made significant contributions to virtually all areas of the discipline, from epistemology and the philosophy of logic to the history of philosophy and the philosophy of science. Part of the fruitfulness of Hintikka’s work is due to its opening important new lines of investigation and new approaches to traditional philosophical problems. This volume gathers together essays from some of Hintikka’s colleagues and former students exploring his influence on their work and pursuing some of the insights that we have found in his work. This book includes a comprehensive overview of Hintikka’s philosophy by Dan Kolak and John Symons and an annotated bibliography of Hintikka’s work.

Download or read book The SAGE Handbook of Service Dominant Logic written by Stephen L. Vargo and published by SAGE. This book was released on 2018-10-08 with total page 1196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Service-Dominant Logic presents a major paradigm shift in thinking about value creation and markets, moving from a ‘goods/product’ logic to a logic that treats the process of service provision as the basis of all exchange, both commercial and social. This timely Handbook brings together chapters written by a stellar cast of expert authors from around the globe, arranged around eleven core themes, to provide a comprehensive overview of key issues, developments, debates and potential future directions for this dynamic field of study: Part 1: Introduction and Background Part 2: Value Cocreation Part 3: Service Exchange Part 4: Service Ecosystems Part 5: Institutions and Institutional Arrangements Part 6: Resources and Resource Integration Part 7: Actors and Practices Part 8: Innovation Part 9: Midrange Theory Part 10: Selected Applications Part 11: Reflections and Prospects This Handbook is an essential reference text for scholars, students, consultants and advanced practitioners across a wide range of business & management practices and academic disciplines.

Download or read book Beyond Duality and Polarization written by Paul Koziey and published by University Press of America. This book was released on 2012-07-13 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beyond Duality and Polarization explores an experience-based learning model, the Phenomenal Patterning approach for personal transformation. Rather than traditional prescriptive learning, methods of personal discovery help us understand how the human mind actually functions. Dr. Koziey introduces two modern Zen skills, watching and catharsis, to increase self-awareness. This frees us from habitual patterns we learned in childhood. We identify the patterns of our own thinking and behaving and see that many of the problems we face are self-created. Repressions are revealed in the shadow psyche and we are able to dissolve our negativity. The overriding message is that when we stop fighting, life starts flowing again.

Download or read book Logic and Its Applications written by Mohua Banerjee and published by Springer Nature. This book was released on 2023-02-22 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023. Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.

Download or read book Lectures on Soft Computing and Fuzzy Logic written by Antonio Di Nola and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume collects selected papers arising from lectures delivered by the authors at the School on Fuzzy Logic and Soft Computing held during the years 1996/97/98/99 and sponsored by the Salerno University. The authors contributing to this volume agreed with editors to write down, to enlarge and, in many cases, to rethink their original lectures, in order to offer to readership, a more compact presentation of the proposed topics. The aim of the volume is to offer a picture, as a job in progress, of the effort that is coming in founding and developing soft computing's techniques. The volume contains papers aimed to report on recent results containing genuinely logical aspects of fuzzy logic. The topics treated in this area cover algebraic aspects of Lukasiewicz Logic, Fuzzy Logic as the logic of continuous t-norms, Intuitionistic Fuzzy Logic. Aspects of fuzzy logic based on similar ity relation are presented in connection with the problem of flexible querying in deductive database. Departing from fuzzy logic, some papers present re sults in Probability Logic treating computational aspects, results based on indishernability relation and a non commutative version of generalized effect algebras. Several strict applications of soft computing are presented in the book. Indeed we find applications ranging among pattern recognition, image and signal processing, evolutionary agents, fuzzy cellular networks, classi fication in fuzzy environments. The volume is then intended to serve as a reference work for foundational logico-algebraic aspect of Soft Computing and for concrete applications of soft computing technologies.

Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2004 with total page 1396 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Toposes Algebraic Geometry and Logic written by F. W. Lawvere and published by Springer. This book was released on 2006-11-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Logics and Falsifications written by Andreas Kapsner and published by Springer. This book was released on 2015-01-07 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne

Download or read book The Logical Writings of Karl Popper written by David Binder and published by Springer Nature. This book was released on 2022-08-07 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.