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. – Contents : – 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; – Includes bibliographical references (p. 218-225) and index.