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1Mathematical Logic

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2An Investigation Of The Laws Of Thought: On Which Are Founded The Mathematical Theories Of Logic ...

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3An Investigation Of The Laws Of Thought, On Which Are Founded Mathematical Theories Of Logic And Probabilities

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4The Mathematical Analysis Of Logic : Being An Essay Towards A Calculus Of Deductive Reasoning

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5Mathematical Logic And The Foundation Of Mathematics; An Introductory Survey

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6A Course On Mathematical Logic

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7Mathematical Introduction To Logic Enderton

Logic

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8Development Of Mathematical Logic

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Logic

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9The Lady Or The Tiger? : And Other Logic Puzzles, Including A Mathematical Novel That Features Gödel's Great Discovery

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ix, 226 p. ; 23 cm

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10Mathematical Logic: Unit 5 Formal Proof

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ix, 226 p. ; 23 cm

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11Kurt Godel MENDELSON Introduction To Mathematical Logic, 6th Ed CRC Press ( 2015)

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Preface - This book is a compact introduction to many of the important topics of mathematical logic, comprising natural and unrestricted set-theoretic methods. Here is a very brief sketch of some of its contents : 1. One of the most prominent features of this new edition is a consistency proof for formal number theory due to Kurt Schütte. This proof had been included in the first edition in 1964.

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12Levels Of Abstraction In Logic And Human Action : A Theory Of Discontinuity In The Structure Of Mathematical Logic, Psychological Behaviour, And Social Organization

Preface - This book is a compact introduction to many of the important topics of mathematical logic, comprising natural and unrestricted set-theoretic methods. Here is a very brief sketch of some of its contents : 1. One of the most prominent features of this new edition is a consistency proof for formal number theory due to Kurt Schütte. This proof had been included in the first edition in 1964.

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13Mathematical Logic And Applications : Proceedings Of The Logic Meeting Held In Kyoto, 1987

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Preface - This book is a compact introduction to many of the important topics of mathematical logic, comprising natural and unrestricted set-theoretic methods. Here is a very brief sketch of some of its contents : 1. One of the most prominent features of this new edition is a consistency proof for formal number theory due to Kurt Schütte. This proof had been included in the first edition in 1964.

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14The Development Of Mathematical Logic

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88 pages 18 cm

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15Archive For Mathematical Logic 1996: Vol 35 Contents

88 pages 18 cm

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16An Investigation Of The Laws Of Thought, On Which Are Founded Mathematical Theories Of Logic And Probabilities

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88 pages 18 cm

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17A Precis Of Mathematical Logic

88 pages 18 cm

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18The Informal Logic Of Mathematical Proof

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Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of Stephen Toulmin [The uses of argument, Cambridge University Press, 1958] and the more recent studies of Douglas Walton, [e.g. The new dialectic: Conversational contexts of argument, University of Toronto Press, 1998]. The focus of both of these approaches has largely been restricted to natural language argumentation. However, Walton's method in particular provides a fruitful analysis of mathematical proof. He offers a contextual account of argumentational strategies, distinguishing a variety of different types of dialogue in which arguments may occur. This analysis represents many different fallacious or otherwise illicit arguments as the deployment of strategies which are sometimes admissible in contexts in which they are inadmissible. I argue that mathematical proofs are deployed in a greater variety of types of dialogue than has commonly been assumed. I proceed to show that many of the important philosophical and pedagogical problems of mathematical proof arise from a failure to make explicit the type of dialogue in which the proof is introduced.

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19ERIC ED055457: A Generalized Instructional System For Elementary Mathematical Logic.

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A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving the use of mechanical theorem-provers for teaching theorem-proving. The entire system is presented here in detail: the program as written in the LISP programing language for a PDP-10 computer. Instructions on how to use the system for research and teaching, block diagrams of key program routines, and example curriculums are included. Enough detail is provided so that versions in other languages for other computer systems may be programed from the information presented here. (Author/JY)

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20DTIC ADA354599: Mathematical Logic And The Foundations Of Mathematics -USSR-

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A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving the use of mechanical theorem-provers for teaching theorem-proving. The entire system is presented here in detail: the program as written in the LISP programing language for a PDP-10 computer. Instructions on how to use the system for research and teaching, block diagrams of key program routines, and example curriculums are included. Enough detail is provided so that versions in other languages for other computer systems may be programed from the information presented here. (Author/JY)

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21Algebra And Logic : Papers From The 1974 Summer Research Institute Of The Australian Mathematical Society, Monash University, Australia

A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving the use of mechanical theorem-provers for teaching theorem-proving. The entire system is presented here in detail: the program as written in the LISP programing language for a PDP-10 computer. Instructions on how to use the system for research and teaching, block diagrams of key program routines, and example curriculums are included. Enough detail is provided so that versions in other languages for other computer systems may be programed from the information presented here. (Author/JY)

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22(Mathematical) Logic For Systems Biology (Invited Paper)

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We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), and should come with (certified) proof tools. Beyond providing a reliable framework, this allows the adequate encodings of our biological systems. We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples. The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq. Future works includes using automatic provers, which would extend existing automatic provers for linear logic. This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience.

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23Mathematical Logic

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"Bibliographical references": p. 325-332

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24Mathematical Logic And Formalized Theories; A Survey Of Basic Concepts And Results

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"Bibliographical references": p. 325-332

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25Archive For Mathematical Logic 1989: Vol 28 Contents

"Bibliographical references": p. 325-332

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26Mathematical Logic

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"Bibliographical references": p. 325-332

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27Algebraic Introduction To Mathematical Logic

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Algebraic Introduction To Mathematical Logic 

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28From Symbolic Logic To Mathematical Logic

Algebraic Introduction To Mathematical Logic 

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29An Introduction To Mathematical Logic

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xi, 212 p. 24 cm

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30Mathematical Logic For Computer Science

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xi, 212 p. 24 cm

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31Mathematical Logic For Computer Science

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xi, 212 p. 24 cm

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32Mathematical Logic

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xi, 212 p. 24 cm

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33Kurt Godel Rautenberg A Concise Introduction To Mathematical Logic Textbook Third Edition Announce

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Foreword - by Lev Beklemishev, Moscow, The field of mathematical logic—evolving around the notions of logical validity, provability, and computation—was created in the first half of the previous century by a cohort of brilliant mathematicians and philosophers such as Frege, Hilbert, Gödel, Turing, Tarski, Malcev, Gentzen, and some others. The development of this discipline is arguably among the highest achievements of science in the twentieth century: it expanded mathematics into a novel area of applications, subjected logical reasoning and computability to rigorous analysis, and eventually led to the creation of computers.

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34Remarks On Mathematical Or Demonstrative Reasoning; Its Connexion With Logic; And Its Application To Science, Physical And Metaphysical, With Reference To Some Recent Publications

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xi, 135 p. 20 cm

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35Mathematical Logic ( Revised Edition) Willard Van Orman Quine

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Mathematical Logic ( Revised Edition) Willard Van Orman Quine

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36Mathematical Logic

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Mathematical Logic ( Revised Edition) Willard Van Orman Quine

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37Mathematical Logic

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Mathematical Logic ( Revised Edition) Willard Van Orman Quine

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38Lectures On Mathematical Logic

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Mathematical Logic ( Revised Edition) Willard Van Orman Quine

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39Sets, Logic, And Mathematical Foundations

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Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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40Mathematical Logic

Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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41Completeness, Compactness, And Undecidability : An Introduction To Mathematical Logic

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Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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42Frege And Gödel : Two Fundamental Texts In Mathematical Logic

Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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43Mathematical Logic And The Foundations Of Mathematics : An Introductory Survey

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Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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44Mathematical Logic And Theoretical Computer Science

Lectures given at a Summer Institute for Teachers of Secondary and College Mathematics, sponsored by the National Science Foundation.

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45A Problem Course In Mathematical Logic

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A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method

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46Artificial Neural Networks And Fuzzy Logic For Recognizing Alphabet Characters And Mathematical Symbols

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Optical Character Recognition software (OCR) are important tools for obtaining accessible texts. We propose the use of artificial neural networks (ANN) in order to develop pattern recognition algorithms capable of recognizing both normal texts and formulae. We present an original improvement of the backpropagation algorithm. Moreover, we describe a novel image segmentation algorithm that exploits fuzzy logic for separating touching characters.

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47Mathematical Logic: Unit 2 Primitive Recursive Functions

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Optical Character Recognition software (OCR) are important tools for obtaining accessible texts. We propose the use of artificial neural networks (ANN) in order to develop pattern recognition algorithms capable of recognizing both normal texts and formulae. We present an original improvement of the backpropagation algorithm. Moreover, we describe a novel image segmentation algorithm that exploits fuzzy logic for separating touching characters.

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48Elements Of Mathematical Logic. (Model Theory)

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Optical Character Recognition software (OCR) are important tools for obtaining accessible texts. We propose the use of artificial neural networks (ANN) in order to develop pattern recognition algorithms capable of recognizing both normal texts and formulae. We present an original improvement of the backpropagation algorithm. Moreover, we describe a novel image segmentation algorithm that exploits fuzzy logic for separating touching characters.

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49Microsoft Research Audio 118380: Mathematical Logic Of Justification

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Since Plato, the notion of justification has been an essential component of epistemic studies. However, until recently, the notion of justification has been conspicuously absent from mathematical models of knowledge within the epistemic logic framework. Commencing from seminal works by von Wright and Hintikka, the notions of Knowledge and Belief have acquired formalization by means of modal logic with modals ‘F is known’ and ‘F is believed.’ Within this approach, the following analysis was adopted: For a given agent, F is known ~ F holds in all epistemically possible situations. The deficiency of this approach is displayed most prominently, in the Logical Omniscience feature of the modal logic of knowledge.

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50Proofs And Refutations : The Logic Of Mathematical Discovery

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Since Plato, the notion of justification has been an essential component of epistemic studies. However, until recently, the notion of justification has been conspicuously absent from mathematical models of knowledge within the epistemic logic framework. Commencing from seminal works by von Wright and Hintikka, the notions of Knowledge and Belief have acquired formalization by means of modal logic with modals ‘F is known’ and ‘F is believed.’ Within this approach, the following analysis was adopted: For a given agent, F is known ~ F holds in all epistemically possible situations. The deficiency of this approach is displayed most prominently, in the Logical Omniscience feature of the modal logic of knowledge.

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  • Title: ➤  Proofs And Refutations : The Logic Of Mathematical Discovery
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