New Directions in Relevant Logic

Igor Sedlár is a researcher at the Institute of Computer Science of the Czech Academy of Sciences in Prague, Czech Republic. After obtaining his PhD at the Comenius University in Bratislava with a thesis on relevant logic in 2009, he was a postdoctoral researcher at the Comenius University, the Slovak Academy of Sciences and the Czech Academy of Sciences. His research focuses on modal and non-classical logics, and includes work on relevant epistemic logic. He has published his results in many top-level conferences and journals, and he is currently pursuing a research project on non-classical dynamic logic funded by the Czech Science Foundation. Shawn Standefer is an assistant professor of Philosophy at National Taiwan University. Before coming to NTU, he was a postdoctoral researcher at the University of Melbourne, and he got his PhD in Philosophy from the University of Pittsburgh. His research focuses on non-classical logics, particularly relevant logics. He has published his research in many peer-reviewed journals and he currently holds a research grant from the National Science and Technology Council of Taiwan. With Greg Restall, he has co-authored an intermediate logic textbook, Logical Methods, published by MIT Press. He is currently working on a book on relevant logics.  Andrew Tedder is a postdoctoral researcher at the Ruhr University Bochum, and has previously held research positions at the University of Vienna and the Czech Academy of Sciences. His research concerns relevant and related non-classical logics, with a focus on quantifiers, modalities, and the application of non-classical logics to metaphysics, information, and formalised mathematical theories. His research has appeared in many peer reviewed journals and he has presented at a wide range of internationally recognised conferences in logic and philosophy.

• Introduction.- Part I: Philosophical Foundations.- Chapter 1. A Hierarchy of Relevance Properties.- Chapter 2. A Topic-Theoretic Perspective on Variable-Sharing (from the Black Sheep of the Family).- Chapter 3. Withered Relevance.- Chapter 4. Variable-Sharing as Relevance.- Part II: Model Theory.- Chapter 5. Algorithmic Corre spondence for Relevance Logics II, Inductive Formulae in Flat Languages for Relevance Logics.- Chapter 6. Quantified Modal Rele vant Logics II, Welcome to the Neighbourhood.- Chapter 7. Semantics for Second Order Relevant Logics.- Chapter 8. Implying and Containing in Truthmaker Semantics.- Chapter 9. The Only 3-valued Logic which is a Natural Implication Expansion with the Variable Sharing Property of Kleene’s Strong Logic.- Part III: Proof Theory.- Chapter 10. A Conceptual Approach to Restricted Quan tification in Relevant Logics.- Chapter 11. Fusion, Fission, and Ackermann’s Truth Constant in Relevant Logics, A Proof-Theoretic Investigation.- Chapter 12. Entailment Generalized.- Chapter 13. Proofs with Star and Perp.- Chapter 14. Morphing Rules of Evaluation into Rules of Deduction: Preserving Relevance and Epistemic Gain.- Part IV: Applications.- Chapter 15. Frege meets Belnap: Basic Law V in a Relevant Logic.- Chapter 16. Explicit and Implicit Belief in First Degree Entailment With Strict Implication.- Chapter 17. Relevant Rational Arithmetic.