Non Axiomatic Logic

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Non Axiomatic Logic A Model Of Intelligent Reasoning

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Author : Wang Pei
language : en
Publisher: World Scientific
Release Date : 2013-05-03

Non Axiomatic Logic A Model Of Intelligent Reasoning written by Wang Pei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-03 with Computers categories.

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 “laws of thought” followed by the human mind. Different from “mathematical” 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 “logical conclusions” 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, etc.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.

Non Axiomatic Logic

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Author : Pei Wang
language : en
Publisher: World Scientific
Release Date : 2013

Non Axiomatic Logic written by Pei Wang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.

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."

Non Axiomatic Reasoning System

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Author : Pei Wang
language : en
Publisher:
Release Date : 1995

Non Axiomatic Reasoning System written by Pei Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Artificial intelligence categories.

Mathematical Logic And Formalized Theories

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Author : Robert L. Rogers
language : en
Publisher: Elsevier
Release Date : 2014-05-12

Mathematical Logic And Formalized Theories written by Robert L. Rogers and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.

Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

Rigid Flexibility

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Author : Pei Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-01

Rigid Flexibility written by Pei Wang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-01 with Computers categories.

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.

Intuition And The Axiomatic Method

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Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-02

Intuition And The Axiomatic Method written by Emily Carson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-02 with Philosophy categories.

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.

Principia Mathematica

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Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927

Principia Mathematica written by Alfred North Whitehead and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

A Friendly Introduction To Mathematical Logic

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Author : Christopher C. Leary
language : en
Publisher: Lulu.com
Release Date : 2015

A Friendly Introduction To Mathematical Logic written by Christopher C. Leary and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Education categories.

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.

First Order Logic

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Author : Fouad Sabry
language : en
Publisher: One Billion Knowledgeable
Release Date : 2023-06-25

First Order Logic written by Fouad Sabry and has been published by One Billion Knowledgeable this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-25 with Computers categories.

What Is First Order Logic First-order logic is a collection of formal systems that are utilized in the fields of mathematics, philosophy, linguistics, and computer science. Other names for first-order logic include predicate logic, quantificational logic, and first-order predicate calculus. In first-order logic, quantified variables take precedence over non-logical objects, and the use of sentences that contain variables is permitted. As a result, rather than making assertions like "Socrates is a man," one can make statements of the form "there exists x such that x is Socrates and x is a man," where "there exists" is a quantifier and "x" is a variable. This is in contrast to propositional logic, which does not make use of quantifiers or relations; propositional logic serves as the basis for first-order logic in this sense. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: First-order logic Chapter 2: Axiom Chapter 3: Propositional calculus Chapter 4: Peano axioms Chapter 5: Universal quantification Chapter 6: Conjunctive normal form Chapter 7: Consistency Chapter 8: Zermelo–Fraenkel set theory Chapter 9: Interpretation (logic) Chapter 10: Quantifier rank (II) Answering the public top questions about first order logic. (III) Real world examples for the usage of first order logic in many fields. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of first order logic.

Rethinking Logic Logic In Relation To Mathematics Evolution And Method

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Author : Carlo Cellucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-09

Rethinking Logic Logic In Relation To Mathematics Evolution And Method written by Carlo Cellucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-09 with Philosophy categories.

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. trigger