This is the first volume of a collection of papers in honor of the fiftieth birthday of Jean-Yves Béziau. These 25 papers have been written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Arnon Avron, John Corcoran, Wilfrid Hodges, Laurence Horn, Lloyd Humbertsone, Dale Jacquette, David Makinson, Stephen Read, and Jan Woleński. It is a state-of-the-art source of cutting-edge studies in the new interdisciplinary field of universal logic. The papers touch upon a wide range of topics including combination of logic, non-classical logic, square and other geometrical figures of opposition, categorical logic, set theory, foundation of logic, philosophy and history of logic (Aristotle, Avicenna, Buridan, Schröder, Mac Coll).
This book offers new perspectives and challenges in the study of logic and will be of interest to all students and researchers interested the nature and future of logic.
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Preface.- Ibn Sina’s Two‐Partite versus Nine‐Partite Logicography by Musa Akrami.- Homotopical categories of logics by Peter Arndt.- Semi‐implication: A Chapter in Universal Logic by Arnon Avron.- A Formal Framework for Hypersequent Calculi and their Fibring by Marcelo Esteban Coniglio and Martin Figallo.- Investigating Knowledge and Opinion by John Corcoran and Idris Samawi Ha.- The Algebra of Opposition (and universal logic interpretations) by Razvan Diaconescu.- Universal Logic as the Science of Patterns by Brian Gaines.- Hexagonal Logic of the Field F8 as a Boolean Logic with Three Involutive Modalities by René Guitart.- The move from one to two quantifiers by Wilfrid Hodges.- On the Contrary: Disjunctive Syllogism and Pragmatic Strengthening by Laurence Horn.- Aristotle on Language and Universal Proof by Jean‐Louis Hudry.- Béziau on And and Or by Lloyd Humberstone.- Universal Logic or Logics in Resemblance Families by Dale Jacquette.- Causality and Attribution in an Aristotelian Theory by Srecko Kovac.- Using Each Other’s Words by Marcus Kracht.- On Universality and Formality in 19th Century Symbolic Logic: The Case of Schröder’s “Absolute Algebra” by Javier Legris.- Caramuel and the “Quantification of the Predicate” by Wolfgang Lenzen.- Lossy Inference Rules and their Bounds: a Brief Review by David Makinson and James Hawthorne.- Nonsets by Daniel Parrochia.- A Roadmap to Decidability by João Rasga, Cristina Sernadas and Amílcar Sernadas.- John Buridan on Non‐Contingency Syllogisms by Stephen Read.- Symbolic Existence in Hugh Mac Coll: a dialogical approach by Juan Redmond.- Beziau’s Contributions to the Logical Geometry of Modalities and Quantifiers by Hans Smessaert and Lorenz Demey.- On Metalogical Pluralism by Vladimir L. Vasyukov.- Constructivism and Metamathematics by Jan Woleński.
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