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  • © 2011

Dual Tableaux: Foundations, Methodology, Case Studies

  • The first book on dual tableaux providing a self-contained presentation of the field and an up-to-date unifying treatment of the research in dual tableaux theory.
  • A number of applications of dual tableaux to contemporary applied theories such as temporal reasoning, spatial reasoning, order-of-magnitude reasoning, fuzzy logic, rough set logics.
  • A reference work to be used by researchers and graduate students.
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (25 chapters)

  1. Front Matter

    Pages i-xvi
  2. Foundations

    1. Front Matter

      Pages 1-1
    2. Dual Tableau for Classical First-Order Logic

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 3-31
    3. Dual Tableaux for Logics of Classical Algebras of Binary Relations

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 33-67
    4. Theories of Point Relations and Relational Model Checking

      • 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. Dual Tableaux for Peirce Algebras

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 85-103
    3. Dual Tableaux for Fork Algebras

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 105-120
    4. Dual Tableaux for Relational Databases

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 121-139
  4. Relational Reasoning in Traditional Non-classical Logics

    1. Front Matter

      Pages 141-141
    2. Dual Tableaux for Classical Modal Logics

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 143-160
    3. Dual Tableaux for Some Logics Based on Intuitionism

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 161-176
    4. Dual Tableaux for Relevant Logics

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 177-194
    5. Dual Tableaux for Many-Valued Logics

      • 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. Dual Tableaux for Information Logics of Plain Frames

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 217-235
    3. Dual Tableaux for Information Logics of Relative Frames

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 237-249
    4. Dual Tableau for Formal Concept Analysis

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 251-261
    5. Dual Tableau for a Fuzzy Logic

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 263-275
    6. Dual Tableaux for Logics of Order of Magnitude Reasoning

      • Ewa Orłowska, Joanna Golińska-Pilarek
      Pages 277-287

About this book

This 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.

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)

Authors and Affiliations

  • National Institute of Telecommunications, Warszawa, Poland

    Ewa Orlowska

  • , Advanced Information Technology, National Institute of Telecommunications, Warszawa, Poland

    Joanna Golińska Pilarek

Bibliographic Information

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access