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 Logical Foundations of Artificial Intelligence written by Michael R. Genesereth and published by Morgan Kaufmann. This book was released on 2012-07-05 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended both as a text for advanced undergraduates and graduate students, and as a key reference work for AI researchers and developers, Logical Foundations of Artificial Intelligence is a lucid, rigorous, and comprehensive account of the fundamentals of artificial intelligence from the standpoint of logic. The first section of the book introduces the logicist approach to AI--discussing the representation of declarative knowledge and featuring an introduction to the process of conceptualization, the syntax and semantics of predicate calculus, and the basics of other declarative representations such as frames and semantic nets. This section also provides a simple but powerful inference procedure, resolution, and shows how it can be used in a reasoning system. The next several chapters discuss nonmonotonic reasoning, induction, and reasoning under uncertainty, broadening the logical approach to deal with the inadequacies of strict logical deduction. The third section introduces modal operators that facilitate representing and reasoning about knowledge. This section also develops the process of writing predicate calculus sentences to the metalevel--to permit sentences about sentences and about reasoning processes. The final three chapters discuss the representation of knowledge about states and actions, planning, and intelligent system architecture. End-of-chapter bibliographic and historical comments provide background and point to other works of interest and research. Each chapter also contains numerous student exercises (with solutions provided in an appendix) to reinforce concepts and challenge the learner. A bibliography and index complete this comprehensive work.
Download or read book Logical Foundations for Rule Based Systems written by Antoni Ligeza and published by Springer Science & Business Media. This book was released on 2006-01-10 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents logical foundations for rule-based systems. An attempt has been made to provide an in-depth discussion of logical and other aspects of such systems, including languages for knowledge representation, inference mechanisms, inference control, design and verification. The ultimate goal was to provide a deeper theoretical insight into the nature of rule-based systems and put together the most complete presentation including details so frequently skipped in typical textbooks. The book may be useful to potentially wide audience, but it is aimed at providing specific knowledge for graduate, post-graduate and Ph.D. students, as well as knowledge engineers and research workers involved in the domain of AI. It also constitutes a summary of the Author’s research and experience gathered through several years of his research work.
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 639 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 The Logical Foundations of Bradley s Metaphysics written by James Allard and published by Cambridge University Press. This book was released on 2004-11-22 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a major contribution to the study of the philosopher F. H. Bradley, the most influential member of the nineteenth-century school of British Idealists. It offers a sustained interpretation of Bradley's Principles of Logic, explaining the problem of how it is possible for inferences to be both valid and yet have conclusions that contain new information. The author then describes how this solution provides a basis for Bradley's metaphysical view that reality is one interconnected experience and how this gives rise to a new problem of truth.
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 Logical Foundations of Computer Science written by Sergei Artemov and published by Springer Science & Business Media. This book was released on 2009-02-13 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2009, held in Deerfield Beach, Florida, USA in January 2008. The volume presents 31 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.
Download or read book The Logical Foundations of the Marxian Theory of Value written by Adolfo García de la Sienra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written before the impressive collapse of the socialist system in Eastern Europe, this book offers a quite objective and serious systematic analysis of the Marxian labor theory of value, Marx's main scientific legacy. After reconstructing the 'prototype' of this theory -- which is the theory as it was left by Marx himself in Capital -- the author proceeds to a careful and detailed analysis of its foundational problems, taking into account Böhm-Bawerk's important criticisms. After introducing advanced contemporary formal tools, the author proceeds to a thorough discussion of the dialectical method, just in order to tackle the foundational problems of the theory. He provides a formally precise and well motivated definition of abstract labor, and then proceeds to prove the existence of a measurement of abstract labor -- i.e. the existence of numerical labor-values. Using this result, the author provides rigorous axiomatic foundations for the theory of value and then proves the existence of a Marxian competitive equilibrium, which is tantamount to the proof of the possibility of reproduction for a capitalist economy. The author finishes the book by showing in detail how the problems of the prototype are solved, by reconstructing the Leontief model of the labor theory of value on the new logical bases. Written in a very clear style, in the language of contemporary philosophy of science, the book is of interest to philosophers of science and economists, applied logicians and all those interested in the scientific legacy of Karl Marx.
Download or read book The Logical Foundations of Cognition written by John Macnamara and published by Oxford University Press. This book was released on 1994-10-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume examines the role of logic in cognitive psychology in light of recent developments, such as Gonzalo Reyes's new semantic theory. Chapters reveal the prospects of applying these new theories to cognitive psychology, cognitive science, linguistics, the philosophy of language and logic.
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 Uncovering the Logic of English A Common Sense Solution to America s Literacy Crisis written by Denise Eide and published by Logic of English, Inc. This book was released on 2011-01-27 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: "English is so illogical!" It is generally believed that English is a language of exceptions. For many, learning to spell and read is frustrating. For some, it is impossible... especially for the 29% of Americans who are functionally illiterate. But what if the problem is not the language itself, but the rules we were taught? What if we could see the complexity of English as a powerful tool rather than a hindrance? --Denise Eide Uncovering the Logic of English challenges the notion that English is illogical by systematically explaining English spelling and answering questions like "Why is there a silent final E in have, large, and house?" and "Why is discussion spelled with -sion rather than -tion?" With easy-to-read examples and anecdotes, this book describes: - the phonograms and spelling rules which explain 98% of English words - how English words are formed and how this knowledge can revolutionize vocabulary development - how understanding the reasons behind English spelling prevents students from needing to guess The author's inspiring commentary makes a compelling case that understanding the logic of English could transform literacy education and help solve America's literacy crisis. Thorough and filled with the latest linguistic and reading research, Uncovering the Logic of English demonstrates why this systematic approach should be as foundational to our education as 1+1=2.
Download or read book Logical Foundations of Proof Complexity written by Stephen Cook and published by Cambridge University Press. This book was released on 2010-01-25 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. The result is a uniform treatment of many systems in the literature.
Download or read book The Logical Foundations of Statistical Inference written by Henry E. Kyburg Jr. and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone knows it is easy to lie with statistics. It is important then to be able to tell a statistical lie from a valid statistical inference. It is a relatively widely accepted commonplace that our scientific knowledge is not certain and incorrigible, but merely probable, subject to refinement, modifi cation, and even overthrow. The rankest beginner at a gambling table understands that his decisions must be based on mathematical ex pectations - that is, on utilities weighted by probabilities. It is widely held that the same principles apply almost all the time in the game of life. If we turn to philosophers, or to mathematical statisticians, or to probability theorists for criteria of validity in statistical inference, for the general principles that distinguish well grounded from ill grounded generalizations and laws, or for the interpretation of that probability we must, like the gambler, take as our guide in life, we find disagreement, confusion, and frustration. We might be prepared to find disagreements on a philosophical and theoretical level (although we do not find them in the case of deductive logic) but we do not expect, and we may be surprised to find, that these theoretical disagreements lead to differences in the conclusions that are regarded as 'acceptable' in the practice of science and public affairs, and in the conduct of business.
Download or read book Logical Foundation of Theoretical Physics written by Gunn Alex Quznetsov and published by Nova Publishers. This book was released on 2006 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the principal properties of spatial-temporal relations are deduced from logical characteristics of information. The objective probability function is obtained from the classical propositional logic by a generalisation of Boolean functions. Fundamental principles of quantum theory are obtained as a result of expressing of event probabilities by spinors.
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 Posing of Questions written by A. Wisniewski and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters.
Download or read book The Collected Works of James M Buchanan written by James M. Buchanan and published by . This book was released on 2002 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: An index to the series "The Collected works of James M. Buchanan."
