Author: Donald W. Loveland
Publisher: Princeton University Press
Release Date: 2014-01-26
Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
Author: Horne, Jeremy
Publisher: IGI Global
Release Date: 2017-05-19
Strong reasoning skills are an important aspect to cultivate in life, as they directly impact decision making on a daily basis. By examining the different ways the world views logic and order, new methods and techniques can be employed to help expand on this skill further in the future. Philosophical Perceptions on Logic and Order is a pivotal scholarly resource that discusses the evolution of logical reasoning and future applications for these types of processes. Highlighting relevant topics including logic patterns, deductive logic, and inductive logic, this publication is an ideal reference source for academicians, students, and researchers that would like to expand their understanding of how society currently employs the use of logical reasoning techniques.
This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal 'Modern Logic', whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis’s association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia. The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.
Author: Keenan Edward L
Publisher: World Scientific
Release Date: 2018-07-06
This book synthesizes the author's work (1980s-2015) on the logical expressive power of natural language. It extends the tools and concepts of model theory as used in (higher order) predicate logic to the study of natural language semantics. It focuses on boolean structure, generalized quantification (separated from variable binding), covering some cases of anaphora. Different categories — predicates, adjective, quantifiers — are modeled by non-isomorphic boolean lattices.Of empirical linguistic interest is the expressibility of many natural classes of quantifiers defined in terms of their logical (automorphism invariant) properties. Some of these correlate with classes used syntactically in generative grammar. In other cases we find general (possibly universal) constraints on possible quantifier denotations in natural language.Also of novel logical interest are entailment paradigms that depend on relations between pairs or triples of generalized quantifier denoting expressions, ones that are in some cases inherently vague. In addition we note novel binary quantifiers that lie beyond the 'Frege boundary' in that they are provably not identical to any iterated application of unary quantifiers.Of philosophical interest is the existence of models which make the same sentences true as standard models but which lack a universe and hence, seemingly, a notion of 'reference'. Moreover, these models generalize to ones in which we can represent (some) intensional expressions without the use of novel ontological objects, such as 'possible worlds' or 'propositions'.
Colburn (computer science, U. of Minnesota-Duluth) has a doctorate in philosophy and an advanced degree in computer science; he's worked as a philosophy professor, a computer programmer, and a research scientist in artificial intelligence. Here he discusses the philosophical foundations of artificial intelligence; the new encounter of science and philosophy (logic, models of the mind and of reasoning, epistemology); and the philosophy of computer science (touching on math, abstraction, software, and ontology).
Author: Peter Paule
Publisher: Springer Science & Business Media
Release Date: 2013-09-17
This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger’s successor as director of the Research Institute for Symbolic Computation.
Author: Roger Simons
Release Date: 2008
For the majority of the twentieth century, philosophers of mathematics focused their attention on foundational questions. However, in the last quarter of the century they began to return to basics, and two new schools of thought were created: social constructivism and structuralism. The advent of the computer also led to proofs and development of mathematics assisted by computer, and to questions concerning the role of the computer in mathematics. This book of sixteen original essays is the first to explore this range of new developments in the philosophy of mathematics, in a language accessible to mathematicians. Approximately half the essays were written by mathematicians, and consider questions that philosophers have not yet discussed. The other half, written by philosophers of mathematics, summarise the discussion in that community during the last 35 years. A connection is made in each case to issues relevant to the teaching of mathematics.
Author: Walter Alexandre Carnielli
Publisher: American Mathematical Soc.
Release Date: 1999
This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society (co-sponsored by the Centre for Logic, Epistemology and the History of Science, State University of Campinas, Sao Paolo) in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians.Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results.
Author: Robert K. Wen
Release Date: 2014-04-28
Philosophy One Mans Overview is for those who have had little contact with the discipline of philosophy but have a persistent interest in the subject, and for those who think recurrently about where they stand in the larger scheme of things. The book aims to expose the reader to a wide array of ideas from the worlds most influential philosophers, aiding him or her to become more perceptive and confident on lifes journey. The book has three segments. The first provides an introduction to philosophy terminology, an explanation of philosophys relevance and usefulness, and a summary of the three major world philosophical traditions the Western, Indian and Chinese. The second discusses the three traditions more substantially, exploring the philosophies of such thinkers as Lao Zi, Aristotle and Kant, and philosophies such as Buddhism, Hinduism, Existentialism and Contemporary New Confucianism (). Finally, the third segment compares the three philosophical traditions. It also includes some thoughts of the author on world peace, as well as on a world viewbased on a deism with Nature as its representation--concerning human character, the living of a life as the purpose of life, and the meaning of death.
Author: Albert R. Meyer
Publisher: Springer Science & Business Media
Release Date: 1989-06-07
The present volume contains the proceedings of Logic at Botik '89, a symposium on logical foundations of computer science organized by the Program Systems Institute of the USSR Academy of Sciences and held at Pereslavl-Zalessky, USSR, July 3-8, 1989. The scope of the symposium was very broad; the topics of interest were: complexity of formal systems, constructive mathematics in computer science, denotational and operational semantics of programs, descriptive complexity, dynamic and algorithmic logics and schematology, formal tools to describe concurrent computations, lambda calculus and related topics, foundations of logic programming, logical foundations of database theory, logics for knowledge representation, modal and temporal logics, type theory in programming, and verification of programs. Thus, the papers in this volume represent many interesting trends in logical foundations of Computer Science, ranging from purely theoretical research to practical applications of theory.
The identity of computing has been fiercely debated throughout its short history. Why is it still so hard to define computing as an academic discipline? Is computing a scientific, mathematical, or engineering discipline? By describing the mathematical, engineering, and scientific traditions of computing, The Science of Computing: Shaping a Discipline presents a rich picture of computing from the viewpoints of the field’s champions. The book helps readers understand the debates about computing as a discipline. It explains the context of computing’s central debates and portrays a broad perspective of the discipline. The book first looks at computing as a formal, theoretical discipline that is in many ways similar to mathematics, yet different in crucial ways. It traces a number of discussions about the theoretical nature of computing from the field’s intellectual origins in mathematical logic to modern views of the role of theory in computing. The book then explores the debates about computing as an engineering discipline, from the central technical innovations to the birth of the modern technical paradigm of computing to computing’s arrival as a new technical profession to software engineering gradually becoming an academic discipline. It presents arguments for and against the view of computing as engineering within the context of software production and analyzes the clash between the theoretical and practical mindsets. The book concludes with the view of computing as a science in its own right—not just as a tool for other sciences. It covers the early identity debates of computing, various views of computing as a science, and some famous characterizations of the discipline. It also addresses the experimental computer science debate, the view of computing as a natural science, and the algorithmization of sciences.