To endow computers with common sense is one of the major long-term goals of Artificial Intelligence research. One approach to this problem is to formalize commonsense reasoning using mathematical ...logic. Commonsense Reasoning is a detailed, high-level reference on logic-based commonsense reasoning. It uses the event calculus, a highly powerful and usable tool for commonsense reasoning, which Erik T. Mueller demonstrates as the most effective tool for the broadest range of applications. He provides an up-to-date work promoting the use of the event calculus for commonsense reasoning, and bringing into one place information scattered across many books and papers. Mueller shares the knowledge gained in using the event calculus and extends the literature with detailed event calculus solutions to problems that span many areas of the commonsense world. * Covers key areas of commonsense reasoning including action, change, defaults, space, and mental states. * The first full book on commonsense reasoning to use the event calculus. * Contextualizes the event calculus within the framework of commonsense reasoning, introducing the event calculus as the best method overall. * Focuses on how to use the event calculus formalism to perform commonsense reasoning, while existing papers and books examine the formalisms themselves. * Includes fully worked out proofs and circumscriptions for every example.
This book provides comprehensive and accessible coverage of the disciplines of philosophy of mathematics and philosophy of logic. After an introduction, the book begins with a historical section, ...consisting of a chapter on the modern period, Kant and his intellectual predecessors, a chapter on later empiricism, including Mill and logical positivism, and a chapter on Wittgenstein. The next section of the volume consists of seven chapters on the views that dominated the philosophy and foundations of mathematics in the early decades of the 20th century: logicism, formalism, and intuitionism. They approach their subjects from a variety of historical and philosophical perspectives. The next section of the volume deals with views that dominated in the later twentieth century and beyond: Quine and indispensability, naturalism, nominalism, and structuralism. The next chapter in the volume is a detailed and sympathetic treatment of a predicative approach to both the philosophy and the foundations of mathematics, which is followed by an extensive treatment of the application of mathematics to the sciences. The last six chapters focus on logical matters: two chapters are devoted to the central notion of logical consequence, one on model theory and the other on proof theory; two chapters deal with the so-called paradoxes of relevance, one pro and one contra; and the final two chapters concern second-order logic (or higher-order logic), again one pro and one contra.
Data Clustering Aggarwal, Charu C; Reddy, Chandan K
2014, 2013, 2018-09-03, 2013-08-21, Volume:
31
eBook
In this book, top researchers from around the world cover the entire area of clustering, from basic methods to more refined and complex data clustering approaches. They pay special attention to ...recent issues in graphs, social networks, and other domains. The book explores the characteristics of clustering problems in a variety of application areas. It also explains how to glean detailed insight from the clustering process--including how to verify the quality of the underlying clusters--through supervision, human intervention, or the automated generation of alternative clusters.
Logic Colloquium '96 Larrazabal, J. M; Lascar, D; Mints, G
03/2017, Volume:
12
eBook
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable ...for years, but they are now in print once again. This volume, the twelfth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association of Symbolic Logic, held at the University of the Basque Country, San Sebastian in July 1996. The main topics were model theory, proof theory, recursion and complexity theory, models of arithmetic, logic for artificial intelligence, formal semantics of natural language, and philosophy of contemporary logic. The volume includes eleven papers from pre-eminent researchers in mathematical logic.
Logic Colloquium '95 Makowsky, Johann A; Ravve, Elena V
03/2017, Volume:
11
eBook
Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable ...for years, but they are now in print once again. This volume, the eleventh publication in the Lecture Notes in Logic series, collects the proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in 1995. It includes papers in the core areas of set theory, model theory, proof theory and recursion theory, as well as the more recent topics of finite model theory and non-monotonic logic. It also includes a tutorial on interactive proofs, zero-knowledge and computationally sound proofs that reported on recent developments in theoretical computer science, and three plenary lectures dedicated to the foundational and technical evolution of set theory over the past 100 years.
While many books have been written about Bertrand Russell's philosophy and some on his logic, I. Grattan-Guinness has written the first comprehensive history of the mathematical background, content, ...and impact of the mathematical logic and philosophy of mathematics that Russell developed with A. N. Whitehead in theirPrincipia mathematica (1910-1913).
This definitive history of a critical period in mathematics includes detailed accounts of the two principal influences upon Russell around 1900: the set theory of Cantor and the mathematical logic of Peano and his followers. Substantial surveys are provided of many related topics and figures of the late nineteenth century: the foundations of mathematical analysis under Weierstrass; the creation of algebraic logic by De Morgan, Boole, Peirce, Schröder, and Jevons; the contributions of Dedekind and Frege; the phenomenology of Husserl; and the proof theory of Hilbert. The many-sided story of the reception is recorded up to 1940, including the rise of logic in Poland and the impact on Vienna Circle philosophers Carnap and Gödel. A strong American theme runs though the story, beginning with the mathematician E. H. Moore and the philosopher Josiah Royce, and stretching through the emergence of Church and Quine, and the 1930s immigration of Carnap and GödeI.
Grattan-Guinness draws on around fifty manuscript collections, including the Russell Archives, as well as many original reviews. The bibliography comprises around 1,900 items, bringing to light a wealth of primary materials.
Written for mathematicians, logicians, historians, and philosophers--especially those interested in the historical interaction between these disciplines--this authoritative account tells an important story from its most neglected point of view. Whitehead and Russell hoped to show that (much of) mathematics was expressible within their logic; they failed in various ways, but no definitive alternative position emerged then or since.
INTRODUCTION TO FUZZY LOGIC Learn more about the history, foundations, and applications of fuzzy logic in this comprehensive resource by an academic leader Introduction to Fuzzy Logic delivers a ...high-level but accessible introduction to the rapidly growing and evolving field of fuzzy logic and its applications. Distinguished engineer, academic, and author James K. Peckol covers a wide variety of practical topics, including the differences between crisp and fuzzy logic, the people and professionals who find fuzzy logic useful, and the advantages of using fuzzy logic. While the book assumes a solid foundation in embedded systems, including basic logic design, and C/C++ programming, it is written in a practical and easy-to-read style that engages the reader and assists in learning and retention. The author includes introductions of threshold and perceptron logic to further enhance the applicability of the material contained within. After introducing readers to the topic with a brief description of the history and development of the field, Introduction to Fuzzy Logic goes on to discuss a wide variety of foundational and advanced topics, like: A review of Boolean algebra, including logic minimization with algebraic means and Karnaugh maps A discussion of crisp sets, including classic set membership, set theory and operations, and basic classical crisp set properties A discussion of fuzzy sets, including the foundations of fuzzy set logic, set membership functions, and fuzzy set properties An analysis of fuzzy inference and approximate reasoning, along with the concepts of containment and entailment and relations between fuzzy subsets Perfect for mid-level and upper-level undergraduate and graduate students in electrical, mechanical, and computer engineering courses, Introduction to Fuzzy Logic covers topics included in many artificial intelligence, computational intelligence, and soft computing courses. Math students and professionals in a wide variety of fields will also significantly benefit from the material covered in this book.
