Logan S.A. Relevance Logic

Cambridge: Cambridge University Press, 2024. — 86 p.Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.Introduction
The Philosophical Picture
Propositional Models
Important Results
Concluding Thoughts
Axiomatizing the Propositional Logic
Metatheory
Extensions of B
Variable Sharing
Variable Sharing in R
Depth Substitution Invariance
Depth Substitution, Philosophically
An Application of Variable Sharing
A Discussion of the Result
Concluding Thoughts on Variable Sharing
First-Order Models
Setup
Details
Important Results
A Bit of Philosophical Reflection
Axiomatizing the First-Order Logic
Addressing a Wo
Metatheory
Soundness
Completeness
A Very Biased and Very Partial Survey of Some Other Topics in the Area
Alternative Semantic Theories
Ternary Relations
Collection Frames
Concluding Thoughts and Other Approaches
Alternative Proof Theories
Fitch Systems
Bunched Systems
Concluding Thoughts
Richer Vocabulary
Modality
Justification Logics
Concluding Thoughts and Other Extensions
Yet More
References
Acknowledgments