An Introduction to Non-Classical Logic

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, paraconsistent, relevant, and fuzzy logics. Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

• Second edition includes sections on tense logic and logics of constrictible negation • Provides new material on relevant logics and fuzzy logics • Much expanded and now in a larger format

Preface to the first edition; Preface to the second edition; Mathematical prolegomenon; Part I. Propositional Logic: 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal modal logics; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Logics with gaps, gluts, and worlds; 10. Relevant logics; 11. Fuzzy logics; 11a. Appendix: many valued modal logics; Postscript: an historical perspective on conditionals; Part II. Qualification and Identity: 12. Classical logic; 13. Free logic; 14. Constant domain modal logics; 15. Variable domain modal logics; 16. Necessary identity in modal logic; 17. Contingent identity in modal logic; 18. Non-normal modal logics; 19. Conditional logics; 20. Intuitionist logic; 21. Many-valued logics; 22. First degree entailment; 23. Logics with gaps, gluts, and worlds; 24. Relevant logics; 25. Fuzzy logics; Postscript: a methodological coda.

\'Priest\'s Introduction to Non-Classical Logic is my textbook of choice for introducing non-classical logic to undergraduates. It is unique in meeting two almost inconsistent aims. It gives the reader an introduction to a vast range of non-classical logics. No comparable textbook manages to cover modal logics, conditional logics, intuitionistic logic, relevant and paraconsistent logics and fuzzy logic with such clarity and accessibility. Amazingly, it is not merely a catalogue of different logical systems. The distinctive value of this Introduction is that it also tells a coherent story: Priest weaves together these different logics in the one narrative - the search for a logic of conditionals. With the publication of the second volume, this unique combination of breadth and coherence now covers much more ground, and the reader now has an expert guide to much more of the vast field of research in non-classical logics.\'

– Greg Restall, The University of Melbourne