TL;DR: In this article, the authors present a survey of modal logics with gaps, gluts, and worlds in the context of Propositional Logic, including many valued modal logic and many-valued logic with first degree entailment.
Abstract: Preface to the first edition Preface to the second edition Mathematical prolegomenon Part I. Propositional Logic: 1. Classical logic and the material conditional 2. Basic modal logic 3. Normal modal logics 4. Non-normal modal logics strict conditionals 5. Conditional logics 6. Intuitionist logic 7. Many-valued logics 8. First degree entailment 9. Logics with gaps, gluts, and worlds 10. Relevant logics 11. Fuzzy logics 11a. Appendix: many valued modal logics Postscript: an historical perspective on conditionals Part II. Qualification and Identity: 12. Classical logic 13. Free logic 14. Constant domain modal logics 15. Variable domain modal logics 16. Necessary identity in modal logic 17. Contingent identity in modal logic 18. Non-normal modal logics 19. Conditional logics 20. Intuitionist logic 21. Many-valued logics 22. First degree entailment 23. Logics with gaps, gluts, and worlds 24. Relevant logics 25. Fuzzy logics Postscript: a methodological coda.
TL;DR: Phenyl urea derivatives having the formula WHEREIN X, n, R1 and R2 have the meanings designated below, and method for controlling unwanted plant growth.
TL;DR: The semantics of entailment in modal logics have been studied in this paper, where a ternary relation R is proposed to take the place for the relevant logics of the Kripke binary relation for standard modal and intuitionistic logics.
Abstract: Publisher Summary This chapter discusses the semantics of entailment. Earlier, modal logics had no semantics. Bearing a real world G, a set of worlds K, and a relation R of relative possibility between worlds, Saul Kripke beheld this situation and saw that it was formally explicable and made model structures. It came to pass that soon everyone was making model structures, and some were deontic, some were temporal, and some were epistemic, according to the conditions on the binary relation R. The models made by Kripke, Hintikka, and Thomason were, however, not relevant. Central to the semantics being developed is a ternary relation R that takes the place for the relevant logics of the Kripke binary relation for standard modal and intuitionistic logics.
TL;DR: Note carefully that the title of this piece is not ‘A Survey of Relevance Logic’; such a project would be impossible given the development of the field and even the space limitations of this Handbook.
Abstract: Note carefully that the title of this piece is not ‘A Survey of Relevance Logic’. Such a project would be impossible given the development of the field and even the space limitations of this Handbook. For example Anderson and Belnap’s [1975] book Entailment: The Logic of Relevance and Necessity, volume 1 runs over 500 pages, and is their summary of just ‘half’ of the work done by them and their co-workers up to about the early 70s.1