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Lattice-Valued Logic

An Alternative Approach to Treat Fuzziness and Incomparability

  • Book
  • © 2003

Overview

Authors:
  1. Yang Xu

    1. Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China

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  2. Keyun Qin

    1. Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China

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  3. Da Ruan

    1. Belgian Nuclear Research Center ( SCK*CEN), Mol, Belgium

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  4. Jun Liu

    1. Department of Mathematics, The University of Manchester Institute of Science and Technology, Manchester, UK

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  • First general introduction on lattice-valued logic
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 132)

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About this book

Lattice-valued Logic aims at establishing the logical foundation for uncertain information processing routinely performed by humans and artificial intelligence systems. In this textbook for the first time a general introduction on lattice-valued logic is given. It systematically summarizes research from the basic notions up to recent results on lattice implication algebras, lattice-valued logic systems based on lattice implication algebras, as well as the corresponding reasoning theories and methods. The book provides the suitable theoretical logical background of lattice-valued logic systems and supports newly designed intelligent uncertain-information-processing systems and a wide spectrum of intelligent learning tasks.

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Table of contents (11 chapters)

  1. Front Matter

    Pages N1-xvi
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 3-24

  3. Lattice Implication Algebras

    1. Front Matter

      Pages 25-25
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    2. Concepts and Properties

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 27-57

    3. Filters

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 59-83

    4. LI-Ideals

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 85-99

    5. Homomorphisms and Representations

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 101-134

    6. Topological Structure of Filter Spaces

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 135-151

    7. Connections with Related Algebras

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 153-169

    8. Related Issues

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 171-204

  4. Lattice-Valued Logic Systems

    1. Front Matter

      Pages 205-205
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    2. Lattice-Valued Propositional Logics

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 207-257

    3. Lattice-Valued First-Order Logics

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 259-304

    4. Uncertainty and Automated Reasoning

      • Yang Xu, Keyun Qin, Da Ruan, Jun Liu
      Pages 305-359

  5. Back Matter

    Pages 361-390
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Authors and Affiliations

  • Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China

    Yang Xu, Keyun Qin

  • Belgian Nuclear Research Center ( SCK*CEN), Mol, Belgium

    Da Ruan

  • Department of Mathematics, The University of Manchester Institute of Science and Technology, Manchester, UK

    Jun Liu

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