Journal of Philosophical Logic

, Volume 22, Issue 5, pp 481–511 | Cite as

Simplified semantics for relevant logics (and some of their rivals)

  • Greg Restall
Article

Abstract

This paper continues the work of Priest and Sylvan inSimplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such asB+ andB. We show that the simplified semantics can also be used for a large number of extensions of the positive base logicB+, and then add the dualising‘*’ operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.

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References

  1. R. Brady, ‘Natural Deduction Systems for some Quantified Relevant Logics’,Logique et Analyse 27 (1984), 355–377.Google Scholar
  2. S. Giambrone and R. Meyer, ‘Completeness and Conservative Extension Results for Some Boolean Relevant Logics’,Studio Logica 48 (1989) 1–14.CrossRefGoogle Scholar
  3. G. Priest and R. Sylvan, ‘Simplified Semantics for Basic Relevant Logics’,Journal of Philosophical Logic 21 (1992), 217–232.CrossRefGoogle Scholar
  4. R. Routley, V. Plumwood, R. Meyer and R. Brady,Relevant Logics and their Rivals, Ridgeview, 1982.Google Scholar
  5. J. Slaney, ‘A General Logic’,Australasian Journal of Philosophy 68 (1990), 74–88.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Greg Restall
    • 1
  1. 1.Philosophy DepartmentThe University of QueenslandAustralia

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