Download or read book Classical Mathematical Logic written by Richard L. Epstein and published by Princeton University Press. This book was released on 2011-12-18 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.
Download or read book The Semantic Foundations of Logic written by Richard L. Epstein and published by . This book was released on 1994 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Propositional Logics written by Richard L. Epstein and published by . This book was released on 2012-06-01 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Download or read book The Semantic Foundations of Logic Volume 1 Propositional Logics written by R.L. Epstein and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.
Download or read book The Semantic Foundations of Logic Volume 1 Propositional Logics written by R.L. Epstein and published by Springer. This book was released on 2014-03-14 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.
Download or read book Propositional Logics written by Richard L. Epstein and published by Oxford University Press, USA. This book was released on 1995 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of my confusion. If logic is objective, how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic that I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the idea that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from reasoning in our usual language is the stepping-stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning that has some objective value.
Download or read book Predicate Logic written by Richard L Epstein and published by Advanced Reasoning Forum. This book was released on 2018-11-05 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The forms and scope of logic rest on assumptions of how language and reasoning connect to experience. In this volume an analysis of meaning and truth provides a foundation for studying modern propositional and predicate logics. Chapters on propositional logic, parsing propositions, and meaning, truth, and reference give a basis for criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples of formalizations of propositions and arguments illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, functions, and second-order logic. The chapter on second-order logic illustrates how different conceptions of predicates and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation, and supplemented by many exercises, this volume is suitable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formalizing reasoning.
Download or read book Predicate Logic written by Richard L. Epstein and published by . This book was released on 2012-05-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Semantic Foundations of Logic written by Richard Louis Epstein and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Fuzzy Logic and Semantic Web Languages Open Access written by Umberto Straccia and published by CRC Press. This book was released on 2016-04-19 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Managing vagueness/fuzziness is starting to play an important role in Semantic Web research, with a large number of research efforts underway. Foundations of Fuzzy Logic and Semantic Web Languages provides a rigorous and succinct account of the mathematical methods and tools used for representing and reasoning with fuzzy information within Semantic
Download or read book Mathematical Aspects of Logic Programming Semantics written by Pascal Hitzler and published by CRC Press. This book was released on 2016-04-19 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.
Download or read book The Semantic Foundations of Logic Predicate logic written by Richard L. Epstein and published by . This book was released on 1994 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic Semantics Metamathematics written by Alfred Tarski and published by Hackett Publishing. This book was released on 1983-01-01 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Procedural Semantics for Hyperintensional Logic written by Marie Duží and published by Springer Science & Business Media. This book was released on 2010-07-01 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds of linguistic context in a fully compositional and anti-contextual way.
Download or read book Foundations of Semantic Web Technologies written by Pascal Hitzler and published by CRC Press. This book was released on 2009-08-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: With more substantial funding from research organizations and industry, numerous large-scale applications, and recently developed technologies, the Semantic Web is quickly emerging as a well-recognized and important area of computer science. While Semantic Web technologies are still rapidly evolving, Foundations of Semantic Web Technologies focuses
Download or read book Propositional Logics 3rd edition written by Richard L Epstein and published by Advanced Reasoning Forum. This book was released on 2018-11-05 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum: as the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Download or read book The Cartesian Semantics of the Port Royal Logic written by John N. Martin and published by Routledge. This book was released on 2019-11-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l’Art de penser, 1662-1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes’ metaphysics. The Logic’s authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book’s central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea’s defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic’s metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting "Aristotelianism," he says virtually nothing about technical concepts in logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 16th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.
