Skip to main content
Log in

R and Relevance Principle Revisited

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

This paper first shows that some versions of the logic R of Relevance do not satisfy the relevance principle introduced by Anderson and Belnap, the principle of which is generally accepted as the principle for relevance. After considering several possible (but defective) improvements of the relevance principle, this paper presents a new relevance principle for (three versions of) R, and explains why this principle is better than the original and others.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson, A.R., & Belnap, N.D. (1962). The pure calculus of entailment. Journal of Symbolic Logic, 27, 19–52.

    Article  Google Scholar 

  2. Anderson, A.R., & Belnap, N.D. (1975). Entailment: The logic of relevance and necessity (Vol. 1). Princeton: Princeton Univ. Press.

    Google Scholar 

  3. Anderson, A.R., Belnap, N.D., Dunn, J.M. (1992). Entailment: The logic of relevance and necessity (Vol. 2). Princeton: Princeton Univ. Press.

    Google Scholar 

  4. Beall, J.C., & Restall, G. (2006). Logical pluralism. Oxford: Oxford Univ. Press.

    Google Scholar 

  5. Brady, R.T. (Ed.) (2003). Relevant logics and their rivals (Vol. 2). Ashgate: Aldershot.

    Google Scholar 

  6. Czelakowski, J. (2001). Protoalgebraic logics. Dordrecht: Kluwer.

    Book  Google Scholar 

  7. Dunn, J.M. (1970). Algebraic completeness for R-Mingle and its extension. Journal of Symbolic Logic, 35, 1–13.

    Article  Google Scholar 

  8. Dunn, J.M. (1986). Relevance logic and entailment. In D. Gabbay, & F. Guenthner (Eds.), Handbook of philosophical logic (pp. 117–224). Dordrecht: Reidel.

    Chapter  Google Scholar 

  9. Dunn, J.M. (2000). Partiality and its dual. Studia Logica, 66, 5–40.

    Article  Google Scholar 

  10. Dunn, J.M., & Restall, G. (2002). Relevance logic. In D. Gabbay, & F. Guenthner (Eds.), Handbook of philosophical logic (Vol. 6, 2nd ed., pp. 1–128). Dordrecht: Reidel.

    Chapter  Google Scholar 

  11. Galatos, N., Jipsen, P., Kowalski, T., Ono, H. (2007). Residuated lattices: An algebraic glimpse at substructural logics. Amsterdam: Elsevier.

    Google Scholar 

  12. Halldén, S. (1951). On the semantic non-completeness of certain Lewis calculi. Journal of Symbolic Logic, 16, 127–129.

    Article  Google Scholar 

  13. Mamide, N. (2002). Substructural logics with mingle. Journal of Logic, Language, and Information, 11, 227–249.

    Article  Google Scholar 

  14. Mares, E.D. (2004). Relevant logic. Cambridge: Cambridge Univ. Press.

    Book  Google Scholar 

  15. Mares, E.D. (2004). “Four-valued” semantics for the relevant logic R. Journal of Philosophical Logic, 33, 327–341.

    Article  Google Scholar 

  16. Metcalfe, G. (2004). Uninorm based logics. In Proceedings of EUROFUSE, 2004 (pp. 85–99). Exit Press.

  17. Metcalfe, G., & Montagna, F. (2007). Substructural fuzzy logics. Journal of Symbolic Logic, 72, 834–864.

    Article  Google Scholar 

  18. Meyer, R.K. (1973). Intuitionism, entailment, negation. In H. Lebranc (Ed.), Truth, syntax, and modality (pp. 168–198). Amsterdam: North-Holland.

    Chapter  Google Scholar 

  19. Meyer, R.K. (1974). New axiomatics for relevant logics. Journal of Philosophical Logic, 3, 53–86.

    Article  Google Scholar 

  20. Meyer, R.K., Giambrone, S., Brady, R.T. (1984). Where gamma fails. Studia Logica, 43, 247–256.

    Article  Google Scholar 

  21. Meyer, R.K., & Routley, R. (1974). Classical relevant logics. Studia Logica, 33, 183–194.

    Article  Google Scholar 

  22. Ono, H. (1998). Proof-theoretic methods in nonclassical logic—an introduction. MJS Memoirs, 2, 207–254.

    Google Scholar 

  23. Read, S. (1988). Relevant logic. Oxford: Basil Blackwell.

    Google Scholar 

  24. Restall, G. (2000). An Introduction to substructural logics. New York: Routledge.

    Google Scholar 

  25. Routley, R., & Meyer, R.K. (1972). The semantics of entailment (III). Journal of Philosophical Logic, 1, 192–208.

    Article  Google Scholar 

  26. Routley, R., & Meyer, R.K. (1973). The semantics of entailment (I). In H. Lebranc (Ed.), Truth, syntax, and modality (pp. 199-243). Amsterdam: North-Holland.

    Chapter  Google Scholar 

  27. Routley, R., Meyer, R.K., Plumwood, V., Brady, R.T. (1982). Relevant logics and their rivals (Vol. 1). California: Ridgeview.

    Google Scholar 

  28. Urquhart, A. (1988). Review on relevant logics and their rivals. Studia Logica, 47, 169–171.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eunsuk Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, E. R and Relevance Principle Revisited. J Philos Logic 42, 767–782 (2013). https://doi.org/10.1007/s10992-012-9247-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-012-9247-1

Keywords

Navigation