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Theory of Graded Consequence

A General Framework for Logics of Uncertainty

  • Book
  • © 2019

Overview

Authors:
  1. Mihir Kumar Chakraborty

    1. University of Calcutta, Kolkata, India

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  2. Soma Dutta

    1. Department of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

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    You can also search for this author in PubMed   Google Scholar

  • Suggests a general scheme for logic of uncertainty
  • Outlines the philosophical grounds for use and mention of a symbol
  • Analyses the metatheory of logic with its distinctive language and interpretation
  • Presents different logics based on user's choice
  • Provides a mathematical model applicable to decision-support systems and approximate reasoning

Part of the book series: Logic in Asia: Studia Logica Library (LIAA)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 1-18

  3. Basics of the Theory of Graded Consequence

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 19-44

  4. Introducing Negation (\(\lnot \)) in the Object Language of the Theory of Graded Consequence

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 45-82

  5. Proof Theoretic Rules in Graded Consequence: From Semantic Perspective

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 83-124

  6. Meta-logical Notions Generalized: Graded Consequence with Fuzzy Set of Premises

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 125-151

  7. Graded Consequence and Consequence in Different Approaches to Fuzzy Logics

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 153-173

  8. Graded Consequence in Decision-Making: A Few Applications

    • Mihir Kumar Chakraborty, Soma Dutta
    Pages 175-218

  9. Back Matter

    Pages 219-224
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Keywords

About this book

This book introduces the theory of graded consequence (GCT) and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels.

Authors and Affiliations

  • University of Calcutta, Kolkata, India

    Mihir Kumar Chakraborty

  • Department of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland

    Soma Dutta

Bibliographic Information

  • Book Title: Theory of Graded Consequence

  • Book Subtitle: A General Framework for Logics of Uncertainty

  • Authors: Mihir Kumar Chakraborty, Soma Dutta

  • Series Title: Logic in Asia: Studia Logica Library

  • DOI: https://doi.org/10.1007/978-981-13-8896-5

  • Publisher: Springer Singapore

  • eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)

  • Copyright Information: Springer Nature Singapore Pte Ltd. 2019

  • Hardcover ISBN: 978-981-13-8894-1Published: 01 August 2019

  • Softcover ISBN: 978-981-13-8987-0Published: 14 August 2020

  • eBook ISBN: 978-981-13-8896-5Published: 22 July 2019

  • Series ISSN: 2364-4613

  • Series E-ISSN: 2364-4621

  • Edition Number: 1

  • Number of Pages: XIII, 224

  • Number of Illustrations: 16 b/w illustrations

  • Topics: Logic, Mathematical Logic and Foundations

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