Skip to main content
SpringerLink
Log in

A second-order relevance logic with modality

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer * operator.

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

    Google Scholar 

  2. A. R. Anderson and N. D. Belnap, Jr., The pure calculus of entailment, The Journal of Symbolic Logic 27 (1962), pp. 19–52.

    Google Scholar 

  3. K. W. Collier, The Story of NR and E, The Relevance Logic Newsletter 1 (1976), pp. 8–10.

    Google Scholar 

  4. M. J. Cresswell, Second-order intensional logic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 18 (1972), pp. 297–320.

    Google Scholar 

  5. Ch. B. Daniels and J. B. Freeman, Classical second-order intensional logic with maximal propositions, Journal of Philosophical Logic 6 (1977), pp. 1–31.

    Google Scholar 

  6. K. Fine, Propositional quantifiers in modal logic, Theoria 36 (1970), pp. 336–346.

    Google Scholar 

  7. G. E. Hughes and M. J. Cresswell, An Introduction to Modal Logic, London; Methuen and Co., Ltd., 1968.

    Google Scholar 

  8. E. Mendelson, Introduction to Mathematical Logic, Princeton; D. van Nostrand Company, Inc., 1964.

    Google Scholar 

  9. R. K. Meyer, Entailment and relevant implication, Logique et Analyse 44 (1968), pp. 472–479.

    Google Scholar 

  10. R. K. Meyer, Intuitionism, entailment, negation, Truth, Syntax, Modality, ed. H. Leblanc, Amsterdam; North-Holland Publishing Co., 1973, pp. 168–198.

    Google Scholar 

  11. R. K. Meyer, J. M. Dunn and H. Leblanc, Completeness of relevant quantification theories, Notre Dame Journal of Formal Logic 15 (1974), pp. 97–121.

    Google Scholar 

  12. R. Routley and R. K. Meyer, The semantics of Entailment I, Truth, Syntax, Modality, see [10], 199–243.

    Google Scholar 

  13. R. Routley and R. K. Meyer, The semantics of Entailment II, Journal of Philosophical Logic 1 (1972), pp. 53–73.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Victoria, Victoria, British Columbia, Canada

    James B. Freeman & Charles B. Daniels

Authors
  1. James B. Freeman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles B. Daniels
    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

Freeman, J.B., Daniels, C.B. A second-order relevance logic with modality. Stud Logica 38, 113–135 (1979). https://doi.org/10.1007/BF00370437

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00370437

Keywords

Search

Navigation