Studia Logica

, Volume 43, Issue 1–2, pp 159–168 | Cite as

A metacompleteness theorem for contraction-free relevant logics

  • John K. Slaney


I note that the logics of the “relevant” group most closely tied to the research programme in paraconsistency are those without the contraction postulate(A→.A→B)→.A→B and its close relatives. As a move towards gaining control of the contraction-free systems I show that they are prime (that wheneverAB is a theorem so is eitherA orB). The proof is an extension of the metavaluational techniques standardly used for analogous results about intuitionist logic or the relevant positive logics.


Research Programme Close Relative Mathematical Logic Analogous Result Computational Linguistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. R. Anderson andN. D. Belnap,Entailment: the Logic of Relevance and Necessity, Vol. I, Princeton University Press, Princeton, 1975.Google Scholar
  2. [2]
    R. K. Meyer,Metacompleteness,Notre Dame Journal of Formal Logic 17 (1976), pp. 501–517.Google Scholar

Copyright information

© Polish Academy of Sciences 1984

Authors and Affiliations

  • John K. Slaney
    • 1
  1. 1.St. Andrews UniversityScotland

Personalised recommendations