Skip to main content
SpringerLink
Log in

An Incomplete Relevant Modal Logic

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

Abstract

The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley–Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (iii) The class of frames for G characterizes the classically based logic T.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. Anderson, A. R. and Belnap, N. D., Jr., Entailment: The Logic of Relevance and Necessity, Vol. I, Princeton University Press, Princeton, NJ, 1975.

    Google Scholar 

  2. Anderson, A. R., Belnap, N. D., Jr. and Dunn, J. M., Entailment: The Logic of Relevance and Necessity, Vol. II, Princeton University Press, Princeton, NJ, 1992.

    Google Scholar 

  3. Fuhrmann, A., Models for relevant modal logics, Studia Logica 49 (1990), 501-514.

    Google Scholar 

  4. Goble, L., A system of modality, Logique et Analyse 12 (1972), 225–237.

    Google Scholar 

  5. Hughes, G. E. and Cresswell, M. J., A New Introduction to Modal Logic, Routledge, London and New York, 1996.

    Google Scholar 

  6. Mares, E. D. and Meyer, R. K., The semantics of R4, J. Philos. Logic 22 (1993), 95–110.

    Google Scholar 

  7. Meyer, R. K. and Mares, E. D., The semantics of entailment 0, in P. Schroeder-Heisterand and K. Dosen (eds), Substructural Logics, Clarendon Press, Oxford, 1993, pp. 239–258.

    Google Scholar 

  8. Routley, R. and Meyer, R. K., The semantics of entailment — II, J. Philos. Logic 1 (1972), 53–73.

    Google Scholar 

  9. Routley, R., Meyer, R. K., Plumwood, V. and Brady, R., Relevant Logics and Their Rivals, Ridgeview, Atascadero, CA, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Willamette University, Salem, OR, 97301, USA

    Lou Goble

Authors
  1. Lou Goble
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goble, L. An Incomplete Relevant Modal Logic. Journal of Philosophical Logic 29, 103–119 (2000). https://doi.org/10.1023/A:1004774422224

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004774422224

Search

Navigation