Logica Universalis

"I find this book extremely useful and important, because it signifies the arrival of a new renaissance in logic, a new revival not only of logic, but of the vision of logic as a unifying tool for science as a whole, including mathematics, physics, cosmology, computer science and AI. The book and the vision behind it give logic, conceived as a scientific study of rationality, new unifying power, new perspectives, and new horizons." Istvan Nemeti, Hungarian Academy of Sciences "Modern logic has been intimately connected with algebra since its origins in figures such as Boole, De Morgan, and Peirce. But while universal algebra is a long recognized field, universal logic has only recently been named as such. This is perhaps because classical logic was until relatively recently taken by many as the "one true logic". But with the proliferation of special purpose non-classical logics in recent years, universal logic is clearly a field whose time has come. This book contains many excellent papers demonstrating the value of this approach." J. Michael Dunn, Indiana University "Modern logic is exploding into manifold applications, and its core research agenda is expanding accordingly. Thus, it becomes of great importance to reflect and rethink the notion of a logical system, which has served us so well for a century now. This book contains timely, broad, and unifying reflections on logical systems and logical consequence, and helps us think where our discipline is going." Johan van Benthem, University of Amsterdam & Stanford University

• Universal Logic: Frameworks and Structures.- From Consequence Operator to Universal Logic: A Survey of General Abstract Logic.- Abstract Model Theory as a Framework for Universal Logic.- A Topological Approach to Universal Logic: Model-Theoretical Abstract Logics.- Selfextensional Logics with Implication.- Logic without Self-Deductibility.- Identity and Nature of Logical Structures.- Equipollent Logical Systems.- What is a Logic?.- What is a Logic, and What is a Proof?.- Tools and Concepts for Universal Logic.- Non-deterministic Matrices and Modular Semantics of Rules.- Two’s Company: “The Humbug of Many Logical Values”.- Friendliness and Sympathy in Logic.- Logical Discrimination.