Nikolaos Galatos received his BS from Aristotle University in Greece and is MS and PhD in Mathematics (2003) from Vanderbilt University in the US. He has held Assistant Professor positions at the Japan Institute of Science and Technology and at Vanderbilt University. Since 2007 he is employed at the University of Denver where he is Professor of Mathematics. His area of research is at the intersection of Universal Algebra, Algebraic Logic and Proof Theory. His work has focused on residuated lattices and substructural logics, exploring the interplay between order algebra and proof theory. He has published more than thirty research articles, served as an editor for a special issue, and coauthored a book.Kazushige Terui received his BA, MS and PhD in Philosophy (2002) from Keio University. He has been an Associate Professor at the National Institute of Informatics in Tokyo and many other visiting positions in Europe. Since 2008 he is an Associate Professor atthe Research Institute for Mathematical Sciences at Kyoto University. His research interests and work areas include Non-classical Logics, Logics in Computer Science, Lambda Calculus, Type Theory, as well as implicit computational complexity. He has published more than thirty articles and served as a program committee member for numerous conferences.

• Chapter 1. A scientific autobiography (Hiroakira Ono).- Part I: Expository and survey chapters.- Chapter 2. Universal algebraic methods for non-classical logics (James G. Raftery).- Chapter 3. Abstract algebraic logic - An introductory chapter (Josep Maria Font).- Chapter 4. Topological duality and algebraic completions (Mai Gehrke).- Chapter 5. An algebraic glimpse at bunched implications and separation logic (Peter Jipsen and Tadeusz Litak).- Part II: Special topics.- Chapter 6. Recognizability in Residuated Lattices (José Gil-Férez and Constantine Tsinakis).- Chapter 7. Finite embeddability property for residuated lattices via regular languages (Rostislav Horčík). Chapter 8. Cover systems for the modalities of linear logic (Robert Goldblatt).- Chapter 9. A negative solution to Ono’s Problem P52: Existence and disjunction properties in intermediate predicate logic (Nobu-Yuki Suzuki).- Chapter 10. Conservative expansions of substructural logics (Jacopo Amidei, Rodolfo C. Ertola-Biraben and Franco Montagna).