Skip to main content
SpringerLink
Log in

On purported Gentzen formulations of two positive relevent logics

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

[10] offers two (cut-free) subscripted Gentzen systems, G 2 T + and G 2 R +, which are claimed to be equivalent in an appropriate sense to the positive relevant logics T + and R +, respectively. In this paper we show that that claim is false. We also show that the argument in [10] for the further claim that cut and/or modus ponens is admissible in two other subscripted Gentzen systems, G 1 T + and G 1 R +, is unsound.

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, Vol. I, Princeton University Press, Princeton, N.J., 1975.

    Google Scholar 

  2. N. D. Belnap, Jr., Display logic, Journal of Philosophical Logic 11 (1982), pp. 375–418.

    Google Scholar 

  3. G. Charlwood, Representations of Semilattice Relevance Logics, University of Toronto Doctoral Dissertation, 1978.

  4. G. Charlwood, An axiomatic version of positive semilattice relevance logic, Journal of Symbolic Logic 46 (1981), pp. 231–39.

    Google Scholar 

  5. J. M. Dunn, Consecution formulation of positive R with co-tenability and t, in [1], pp. 381–91.

    Google Scholar 

  6. S. Giambrone, Gentzen Systems and Decision Procedures for Relevant Logics, Australian National University Doctoral Dissertation, Canberra, 1983.

  7. S. Giambrone, A critique of ‘Decision procedures for two positive relevance logics’, forthcoming.

  8. S. Giambrone, Subscripted Gentzen systems for semilattice logics, in preparation.

  9. A. Kron, Decision procedures for two positive relevance logics, Reports on Mathematical Logic 19 (1978), pp. 61–78.

    Google Scholar 

  10. A. Kron, Gentzen formulations of two positive relevance logics, Studia Logica 39 (1980), pp. 381–403.

    Google Scholar 

  11. A. Kron, Gentzen formulations of two positive relevance logics (correction), Studia Logica 40 (1981), p. 311.

    Google Scholar 

  12. G. E. Minc, Cut-elimination theorem for relevant logics, Journal of Soviet Mathematics 6 (1976), pp. 422–28.

    Google Scholar 

  13. A. Urquhart, The Semantics of Entailment, University of Pittsburgh Doctoral Dissertation, 1973.

  14. A. Urquhart, Semantics for relevant logics, Journal of Symbolic Logic 37 (1972), pp. 159–69.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Southwestern Louisiana, 70504, Lafayette, Louisiana, USA

    Steve Giambrone

Authors
  1. Steve Giambrone
    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

Giambrone, S. On purported Gentzen formulations of two positive relevent logics. Stud Logica 44, 233–236 (1985). https://doi.org/10.1007/BF00394443

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00394443

Keywords

Search

Navigation