Logica Universalis: Towards a General Theory of Logic

✍ Scribed by Jean-Yves Beziau

• Publisher: Birkhäuser Basel
• Year: 2005
• Tongue: English
• Leaves: 225
• Edition: 1
• Category: Library

✦ Synopsis

Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.

✦ Table of Contents

Contents......Page 5
Preface......Page 7
Part I. Universal Logic: Frameworks and Structures......Page 11
From Consequence Operator to Universal Logic: A Survey of General Abstract Logic......Page 12
Abstract Model Theory as a Framework for Universal Logic......Page 27
A Topological Approach to Universal Logic: Model-Theoretical Abstract Logics......Page 42
Selfextensional Logics with Implication......Page 71
Logic without Self-Deductibility......Page 95
Part II. Identity and Nature of Logical Structures......Page 102
Equipollent Logical Systems......Page 103
What is a Logic?......Page 116
What is a Logic, and What is a Proof?......Page 137
Part III. Tools and Concepts for Universal Logic......Page 148
Non-deterministic Matrices and Modular Semantics of Rules......Page 149
Two’s Company: “The Humbug of Many Logical Values”......Page 168
Logical Friendliness and Sympathy......Page 189
Logical Discrimination......Page 204