Relevant Logic A Philosophical Interpretation

The defining feature of relevant logic is that it forces the premises of an argument to be really used and thus become "relevant" in deriving its conclusion. This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The logic is analyzed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book concludes by examining various applications of relevant logic.

This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book ends by examining various applications of relevant logic and presenting some interesting open problems. It will be of interest to a range of readers including advanced students of logic, philosophical and mathematical logicians, and computer scientists.

Preface; Acknowledgements; Part I. Relevant Logic and its Semantics: 1. What is relevant logic and why do we need it?; 2. Possible worlds and beyond; 3. Situating implication; 4. Ontological interlude; 5. Negation; 6. Modality, entailment and quantification; Part II. Conditionals: 7. Indicative conditionals; 8. Counterfactuals; Part III. Inference and its Applications: 9. The structure of deduction; 10. Disjunctive syllogism; 11. Putting relevant logic to work; 12. Afterword; Appendix A: the logic R; Appendix B: Routley-Meyer semantics for R; Glossary; References; Index.

This book introduces the reader to relevant logic and provides the subject with a philosophical interpretation. It offers a systematic account of the motivation, key features and applications of this type of logic, with particular emphasis on its philosophical dimension.

Edwin D. Mares is Senior Lecturer at the Philosophy Programme, Victoria University of Wellington. He has published extensively on both the philosophical and mathematical aspects of logic, as well as metaphysics and the philosophy of language.