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Full Description
This book brings together contemporary work on relevant logics to showcase the recent progress of the field and set the stage for future research. The papers in the volume contribute to the formal and philosophical development of the field. They include contributions from different traditions and approaches ranging from philosophical discussions of the foundations of relevant, and related kinds of non-classical, logic to mathematical work concerning open technical problems in the field. This is the first edited collection on the topic in many years, and it includes contributions from established figures as well as younger generations of researchers. Relevant logics have recently seen a resurgence of interest and this volume will be an important resource for logicians working on substructural and relevant logics for years to come.
Contents
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.
