This book is a collection of contributions honouring Arnon Avrons seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics.

Avrons foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avrons past and present works. This book is of interest to computer scientists and scholars of formal logic.

Ofer Arieli is a professor of Computer Science at the School of Computer Science, the Academic College of Tel-Aviv. He received his B.Sc. in Mathematics and Computer Science from the Hebrew University in Jerusalem, and M.Sc. and Ph.D. in Computer Science from Tel-Aviv University. Afterwards (20002001) he was a postdoc researcher at the Department of Computer Science, the University of Leuven, Belgium. His main research interests are related to the applications of non-classical logics in artificial intelligence and to reasoning with incomplete and inconsistent information.
 Anna Zamansky is an associate professor at the Information Systems Department, University of Haifa. She received her B.A. and M.Sc. in Computer Science from the Technion, Israeli Institute of Technology, and her Ph.D. in Computer Science from Tel-Aviv University. Afterwards (20102012) she was a Marie Curie postdoctoral researcher in the Computational Logic group at the Technical University of Vienna, Austria. Her research interests include applied logic and reasoning with inconsistent information.

Chapter 1. An uncertain road to certainty; Arnon Avron.- Chapter 2. Introduction: Non-classical logics Between semantics and proof theory (In relation to Arnon Avrons work); Ofer Arieli and Anna Zamansky.- Chapter 3. Interpretations of weak positive modal logics; Katalin Bimbó.- Chapter 4. On axioms and rexpansions; Carlos Caleiro and Sérgio Marcelin.- Chapter 5. Credal calculi, evidence, and consistency; Walter Carnielli and Juliana Bueno-Soler.- Chapter 6. Theorems of alternatives for substructural logics; Almudena Colacito, Nikolaos Galatos and George Metcalfe.- Chapter 7. Degree-preserving Gödel logics with aninvolution: intermediate logics and (ideal) paraconsistency; Marcelo E. Coniglio, Francesc Esteva, Joan Gispert and Lluis Godo.- Chapter 8. R-mingle is nice, and so is Arnon Avron; J. Michael Dunn.- Chapter 9.The strict/tolerant idea and bilattices; Melvin Fitting.- Chapter 10. What is negation in a system 2020?; Dov Gabbay.- Chapter 11.Relevance Domains and the Philosophy of Science; Edwin Mares.- Chapter 12. Consequence relations with real truth-values; Daniele Mundici.- Chapter 13. Geometric rules in infinitary logic; Sara Negri.- Chapter 14. Connexive variants of modal logics over FDE; Sergei Odinstov, Daniel Skurt and Heinrich Wansing.- Chapter 15. Comments on the Papers; Arnon Avron.- Chapter 16. Arnon Avron - List of publications.