Download or read book The Logical Foundations of Mathematics written by William S. Hatcher and published by Elsevier. This book was released on 2014-05-09 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Logical Foundations of Mathematics offers a study of the foundations of mathematics, stressing comparisons between and critical analyses of the major non-constructive foundational systems. The position of constructivism within the spectrum of foundational philosophies is discussed, along with the exact relationship between topos theory and set theory. Comprised of eight chapters, this book begins with an introduction to first-order logic. In particular, two complete systems of axioms and rules for the first-order predicate calculus are given, one for efficiency in proving metatheorems, and the other, in a "natural deduction" style, for presenting detailed formal proofs. A somewhat novel feature of this framework is a full semantic and syntactic treatment of variable-binding term operators as primitive symbols of logic. Subsequent chapters focus on the origin of modern foundational studies; Gottlob Frege's formal system intended to serve as a foundation for mathematics and its paradoxes; the theory of types; and the Zermelo-Fraenkel set theory. David Hilbert's program and Kurt Gödel's incompleteness theorems are also examined, along with the foundational systems of W. V. Quine and the relevance of categorical algebra for foundations. This monograph will be of interest to students, teachers, practitioners, and researchers in mathematics.
Download or read book Foundations of the Logical Theory of Scientific Knowledge Complex Logic written by A.A. Zinov'ev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boston Studies in the Philosophy of Science are devoted to symposia, con gresses, colloquia, monographs and collected papers on the philosophical foundations of the sciences. It is now our pleasure to include A. A. Zi nov'ev's treatise on complex logic among these volumes. Zinov'ev is one of the most creative of modern Soviet logicians, and at the same time an innovative worker on the methodological foundations of science. More over, Zinov'ev, although still a developing scholar, has exerted a sub stantial and stimulating influence upon his colleagues and students in Moscow and within other philosophical and logical circles of the Soviet Union. Hence it may be helpful, in bringing this present work to an English-reading audience, to review briefly some contemporary Soviet investigations into scientific methodology. During the 1950's, a vigorous new research program in logic was under taken, and the initial published work -characteristic of most Soviet pub lications in the logic and methodology of the sciences - was a collection of essays, Logical Investigations (Moscow, 1959). Among the authors, in addition to Zinov'ev himself, were the philosophers A. Kol'man and P. V. Tavanec, and the mathematicians and linguists, S. A. Janovskaja, A. S. Esenin-Vol'pin, S. K. Saumjan, G. N. Povarov.
Download or read book The Logical Foundations of Science written by W. E. Johnson and published by . This book was released on 1924 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic written by William E. Johnson and published by . This book was released on 1964 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Logical Foundations of Cognition written by John Macnamara and published by Oxford University Press, USA. This book was released on 1994 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book presents seminal contributions to the emerging synthesis of logic and cognitive psychology. In collaboration with several colleagues the editors have developed a landmark semantic theory for natural languages.
Download or read book The Logical Foundations of Scientific Theories written by Decio Krause and published by Routledge. This book was released on 2016-07-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.
Download or read book The Logical Foundations of Science written by W. E. Johnson and published by . This book was released on 1924 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The logical foundations of science written by William Ernest Johnson and published by . This book was released on 1964 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic Pt 3 The Logical Foundations of Science written by W.E. Johnson and published by . This book was released on 1924 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logic Part Iii the Logical Foundations of Science written by and published by CUP Archive. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knowledge in Action written by Raymond Reiter and published by MIT Press. This book was released on 2001-07-27 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Specifying and implementing dynamical systems with the situation calculus. Modeling and implementing dynamical systems is a central problem in artificial intelligence, robotics, software agents, simulation, decision and control theory, and many other disciplines. In recent years, a new approach to representing such systems, grounded in mathematical logic, has been developed within the AI knowledge-representation community. This book presents a comprehensive treatment of these ideas, basing its theoretical and implementation foundations on the situation calculus, a dialect of first-order logic. Within this framework, it develops many features of dynamical systems modeling, including time, processes, concurrency, exogenous events, reactivity, sensing and knowledge, probabilistic uncertainty, and decision theory. It also describes and implements a new family of high-level programming languages suitable for writing control programs for dynamical systems. Finally, it includes situation calculus specifications for a wide range of examples drawn from cognitive robotics, planning, simulation, databases, and decision theory, together with all the implementation code for these examples. This code is available on the book's Web site.
Download or read book Logical Foundations of Cyber Physical Systems written by André Platzer and published by Springer. This book was released on 2018-07-30 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cyber-physical systems (CPSs) combine cyber capabilities, such as computation or communication, with physical capabilities, such as motion or other physical processes. Cars, aircraft, and robots are prime examples, because they move physically in space in a way that is determined by discrete computerized control algorithms. Designing these algorithms is challenging due to their tight coupling with physical behavior, while it is vital that these algorithms be correct because we rely on them for safety-critical tasks. This textbook teaches undergraduate students the core principles behind CPSs. It shows them how to develop models and controls; identify safety specifications and critical properties; reason rigorously about CPS models; leverage multi-dynamical systems compositionality to tame CPS complexity; identify required control constraints; verify CPS models of appropriate scale in logic; and develop an intuition for operational effects. The book is supported with homework exercises, lecture videos, and slides.
Download or read book Logic written by W. E. Johnson and published by . This book was released on 1964 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Logical Foundations of Mathematics and Computational Complexity written by Pavel Pudlák and published by Springer Science & Business Media. This book was released on 2013-04-22 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Download or read book Logic written by W. E. Johnson and published by Cambridge University Press. This book was released on 2014-04-17 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1924, this book forms the third of a three-volume series relating to 'the whole field of logic as ordinarily understood'.
