New Essays on Belnap-­Dunn Logic

  • Hitoshi Omori
  • Heinrich Wansing

Part of the Synthese Library book series (SYLI, volume 418)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Hitoshi Omori, Heinrich Wansing
    Pages 1-9
  3. Essays by the Founders

    1. Front Matter
      Pages 11-11
    2. J. Michael Dunn
      Pages 13-19
    3. Nuel D. Belnap
      Pages 35-53
    4. Nuel D. Belnap
      Pages 55-76
    5. Nuel D. Belnap, Heinrich Wansing
      Pages 99-111
  4. New Essays

About this book


This edited volume collects essays on the four-valued logic known as Belnap-Dunn logic, or first-degree entailment logic (FDE). It also looks at various formal systems closely related to it. These include the strong Kleene logic and the Logic of Paradox. Inside, readers will find reprints of seminal papers written by the fathers of the field: Nuel Belnap and Michael Dunn. In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn.

Besides the original, monumental papers, the book also includes research by leading scholars. They consider the extraordinary importance of Belnap-Dunn logic from several perspectives. They look at how, philosophically, it has served as a basic system of inconsistency-tolerant reasoning, as the core of underlying logics for theories based on dialetheism, and, more recently, for theories based on Buddhist philosophy. Coverage also explores its contributions to computer science, such as knowledge representation and information processing.

This mix of seminal papers and insightful analysis by top scholars offers readers a comprehensive outlook on Belnap-Dunn logic and its related expansions, which have been agenda setting for the debate on philosophical logic as well as philosophy of logic. The book will also enhance further discussion on the philosophical issues related to nonclassical logics in general.


Belnap’s four-­‐valued semantics Dunn’s two-­‐valued semantics Expansions of Belnap-­‐Dunn logic Relevant logic a la American plan Relevant logic a la Australian plan Logic of information structures Nonclassical truth theory Nonclassical mathematics Logic for Buddhist philosophy Logic for dialetheism Natural deduction Paraconsistency Paracompleteness first-degree entailment logic Kleene logic Logic of Paradox inconsistency-tolerant reasoning theories based on dialetheism

Editors and affiliations

  • Hitoshi Omori
    • 1
  • Heinrich Wansing
    • 2
  1. 1.Ruhr-University BochumBochumGermany
  2. 2.Ruhr-University BochumBochumGermany

Bibliographic information