New Directions in Relevant Logic

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.