Hiroakira Ono on Substructural Logics

1. Front Matter

   Pages i-xii

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2. A Scientific Autobiography

   • Hiroakira Ono

   Pages 1-23

3. Expository and Survey Chapters

   1. Front Matter

      Pages 25-25

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   2. Universal Algebraic Methods for Non-classical Logics

      • James G. Raftery

      Pages 27-70

   3. Abstract Algebraic Logic

      • Josep Maria Font

      Pages 71-142

   4. Topological Duality and Algebraic Completions

      • Mai Gehrke

      Pages 143-184

   5. An Algebraic Glimpse at Bunched Implications and Separation Logic

      • Peter Jipsen, Tadeusz Litak

      Pages 185-242

4. Special Topics

   1. Front Matter

      Pages 243-243

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   2. Recognizability in Residuated Lattices

      • José Gil-Férez, Constantine Tsinakis

      Pages 245-271

   3. Finite Embeddability Property for Residuated Lattices via Regular Languages

      • Rostislav Horčík

      Pages 273-298

   4. Cover Systems for the Modalities of Linear Logic

      • Robert Goldblatt

      Pages 299-318

   5. A Negative Solution to Ono’s Problem P52: Existence and Disjunction Properties in Intermediate Predicate Logics

      • Nobu-Yuki Suzuki

      Pages 319-337

   6. Conservative Expansions of Substructural Logics

      • Jacopo Amidei, Rodolfo C. Ertola-Biraben, Franco Montagna

      Pages 339-368

5. Back Matter

   Pages 369-375

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This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science.

It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions.  This book will be primarily of interest to researchers working in algebraic and non-classical logic.

• Substructural Logics
• Residuated Lattices
• Algebraic Logic
• Duality Theory
• Universal Algebra
• Bunched Implication Logic
• Formal Languages
• Ordered Algebra
• Intermediate Logics
• Full Lambek Calculus

• Department of Mathematics, University of Denver, Denver, USA

  Nikolaos Galatos

• Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

  Kazushige Terui

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.

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