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© 2011

Dual Tableaux: Foundations, Methodology, Case Studies

Book

Part of the Trends in Logic book series (TREN, volume 33)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Foundations

    1. Front Matter
      Pages 1-1
    2. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 3-31
    3. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 33-67
    4. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 69-82
  3. Reasoning in Logics of Non-classical Algebras of Relations

    1. Front Matter
      Pages 83-83
    2. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 85-103
    3. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 105-120
    4. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 121-139
  4. Relational Reasoning in Traditional Non-classical Logics

    1. Front Matter
      Pages 141-141
    2. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 143-160
    3. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 161-176
    4. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 177-194
    5. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 195-213
  5. Relational Reasoning in Logics of Information and Data Analysis

    1. Front Matter
      Pages 215-215
    2. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 217-235
    3. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 237-249
    4. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 251-261
    5. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 263-275
    6. Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 277-287

About this book

Introduction

The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory.

Keywords

Dual tableau Logic Proof theory Relation algebra

Authors and affiliations

  1. 1.National Institute of TelecommunicationsWarszawaPoland
  2. 2., Advanced Information TechnologyNational Institute of TelecommunicationsWarszawaPoland

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

“This book is an excellent guide for a unified treatment of the many logics surveyed … . this book unifies a collection of topics and systems that are hard to find elsewhere, and testifies to the increasing interest in non-classical logic. … Overall, it is undoubtedly a book to have in your library.” (Walter Carnielli, Studia Logica, Vol. 101, 2013)

“This book surveys the theory and applications of the method of dual tableaux introduced by Rasiowa and Sikorski in the 1960s. A broad range of theories have been studied using this framework, and most of them are included here. … Overall, the book introduces a thorough and in-depth study of the different applications of the framework of dual tableaux.” (Manuel Ojeda-Aciego, Mathematical Reviews, Issue 2012 f)

“Providing a reference for researchers and students, this book presents the fundamental concepts of dual tableaux and a wide scope of applications. These include logic methods used in mathematics and philosophy as well as applied theories of computational logic.” (Branislav Boričić, Zentralblatt MATH, Vol. 1210, 2011)