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 In addition, the collection also features a well-known but previously unpublished manuscript of Dunn, an interview with Belnap, and a new essay by Dunn.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 tocomputer 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.

Hitoshi Omori is a postdoctoral researcher in logic at Kyoto University (Japan). He took his M.A. and Ph.D. in Logic at Tokyo Institute of Technology (Japan). After the completion of Ph.D., he was a postdoctoral researcher at Kobe University (Japan) and City University of New York (USA) before coming to Kyoto. His main interest is in philosophical logic, including paraconsistent, many-valued and modal logics, and dialetheism. Website: https://sites.google.com/site/hitoshiomori/home
Heinrich Wansing is a Professor of Logic and Epistemology at the Ruhr-University Bochum (Germany). Before that he was a Professor of Philosophy of Science and Logic at Dresden University of Technology (19992010). He took his M.A. and his Ph.D. in Philosophy at the Free University of Berlin and his Habilitation in logic and analytical philosophy at the University of Leipzig. He is the author of The Logic of Information Structures (Springer 1993), Displaying Modal Logic (Kluwer 1998), Truth and Falsehood. An Inquiry into Generalized Logical Values (with Y. Shramko, Springer 2011), Proof Theory of N4-related Paraconsistent Logics (with K. Kamide, College Publications 2015) and numerous articles in professional journals. Heinrich Wansing has been working mainly on philosophical logic, including the semantics and proof theory of modal, constructive, paraconsistent, many-valued, and other nonclassical logics. Moreover, he is the Editor-in-Chief of the book series Trends in Logic (Springer), a managing editor of the journal Studia Logica, and a member of a number of other editorial boards of logic and philosophy journals. Website: http://www.ruhr-uni-bochum.de/philosophy/logic/

An invitation to New Essays on Belnap-Dunn logic (Hitoshi Omori and Heinrich Wansing).- Part I. Essays by the Founders. Natural Language versus Formal Language (J. Michael Dunn).- Intuitive Semantics for First-Degree Entailment and Coupled Trees (J. Michael Dunn).- How a Computer Should Think (Nuel D. Belnap).- A Useful Four-Valued Logic (Nuel D. Belnap).- Two, Three, Four, Infinity: The Path to the Four-valued Logic and Beyond (J. Michael Dunn).- Interview with Prof. Nuel D. Belnap (Nuel D. Belnap and Heinrich Wansing).- Part II. New Essays. FDE as the One True Logic (Jc Beall).- Default Rules in the Logic of First-Degree Entailments (Katalin Bimbó).- Belnap and Nagarjuna on How Computers and Sentient Beings Should Think: Truth, Trust and the Catuskoti (Jay L. Garfield).- K3, 3, LP, RM3, A3, FDE, M: How to Make Many-Valued LogicsWork for You (Allen P. Hazen and Francis Jeffry Pelletier).- FDE as a Base for Constructive Logic (Andreas Kapsner).- Bridging the Two Plans in the Semantics for Relevant Logic (Takuro Onishi).- Bilattice Logics and Demi-Negation (Francesco Paoli).- Consistency, Completeness, and Classicality (Adam Prenosil).- Natural Deduction Systems for Logics in the FDE Family (Graham Priest).- Modelling Sources of Inconsistent Information in Paraconsistent Modal Logic (Igor Sedlár and Ondrej Majer).- First-Degree Entailment and Structural Reasoning (Yaroslav Shramko).