Non Axiomatic Logic
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| Author | : Pei Wang |
| Publisher | : World Scientific |
| Total Pages | : 275 |
| Release | : 2013 |
| Genre | : Computers |
| ISBN | : 9814440280 |
This book provides a systematic and comprehensive description of Non-Axiomatic Logic, which is the result of the author''s research for about three decades.Non-Axiomatic Logic is designed to provide a uniform logical foundation for Artificial Intelligence, as well as an abstract description of the OC laws of thoughtOCO followed by the human mind. Different from OC mathematicalOCO logic, where the focus is the regularity required when demonstrating mathematical conclusions, Non-Axiomatic Logic is an attempt to return to the original aim of logic, that is, to formulate the regularity in actual human thinking. To achieve this goal, the logic is designed under the assumption that the system has insufficient knowledge and resources with respect to the problems to be solved, so that the OC logical conclusionsOCO are only valid with respect to the available knowledge and resources. Reasoning processes according to this logic covers cognitive functions like learning, planning, decision making, problem solving, This book is written for researchers and students in Artificial Intelligence and Cognitive Science, and can be used as a textbook for courses at graduate level, or upper-level undergraduate, on Non-Axiomatic Logic."
| Author | : Alfred North Whitehead |
| Publisher | : |
| Total Pages | : 688 |
| Release | : 1910 |
| Genre | : Logic, Symbolic and mathematical |
| ISBN | : |
| Author | : Christopher C. Leary |
| Publisher | : Lulu.com |
| Total Pages | : 382 |
| Release | : 2015 |
| Genre | : Computers |
| ISBN | : 1942341075 |
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
| Author | : Pei Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 2006-09-01 |
| Genre | : Computers |
| ISBN | : 1402050453 |
This book is the most comprehensive description of the decades-long Non-Axiomatic Reasoning System (NARS) project, including its philosophical foundation, methodological consideration, conceptual design details, implications in the related fields, and its similarities and differences to many related works in cognitive science. While most current works in Artificial Intelligence (AI) focus on individual aspects of intelligence and cognition, NARS is designed and developed to attack the AI problem as a whole.
| Author | : Volker Halbach |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 2014-02-27 |
| Genre | : Philosophy |
| ISBN | : 1316584232 |
At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.
| Author | : J. Barkley Rosser |
| Publisher | : Courier Dover Publications |
| Total Pages | : 587 |
| Release | : 2008-12-18 |
| Genre | : Mathematics |
| ISBN | : 0486468984 |
Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
| Author | : Patrick Suppes |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-05-04 |
| Genre | : Mathematics |
| ISBN | : 0486136876 |
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
| Author | : Petr Hájek |
| Publisher | : Cambridge University Press |
| Total Pages | : 475 |
| Release | : 2017-03-02 |
| Genre | : Mathematics |
| ISBN | : 1107168414 |
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
| Author | : Torkel Franzén |
| Publisher | : Cambridge University Press |
| Total Pages | : 318 |
| Release | : 2017-03-30 |
| Genre | : Mathematics |
| ISBN | : 1108641636 |
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 sixteenth publication in the Lecture Notes in Logic series, gives a sustained presentation of a particular view of the topic of Gödelian extensions of theories. It presents the basic material in predicate logic, set theory and recursion theory, leading to a proof of Gödel's incompleteness theorems. The inexhaustibility of mathematics is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results are introduced as needed, making the presentation self-contained and thorough. Philosophers, mathematicians and others will find the book helpful in acquiring a basic grasp of the philosophical and logical results and issues.
| Author | : Richard W. Kaye |
| Publisher | : Cambridge University Press |
| Total Pages | : 12 |
| Release | : 2007-07-12 |
| Genre | : Mathematics |
| ISBN | : 1139467212 |
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
