Journal of Philosophical Logic

, Volume 24, Issue 2, pp 139–160 | Cite as

Four-valued semantics for relevant logics (and some of their rivals)

  • Greg Restall
Article

Abstract

This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the ‘Australian Plan’ semantics, which uses a unary operator ‘⋆’ for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a semantics for the contraction-free relevant logicC (orRW). Unfortunately, its approach seems to model little else. The third approach seems to capture a wide range of formal systems, but at the time of writing, lacks a completeness proof.

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References

  1. Belnap, N. D., Jr. (1977), ‘A Useful Four-Valued Logic,’ in J.M Dunn and G. Epstein (eds),Modern Uses of Multiple-Valued Logic, Dordrecht, 8–37.Google Scholar
  2. Belnap, N. D., Jr. (1977), ‘How a Computer Should Think,’ in G. Ryle (ed.),Contemporary Aspects of Philosophy, Oriel Press, 30–55.Google Scholar
  3. Dunn, J. M. (1976), ‘Intuitive Semantics for First-Degree Entailment and ‘Coupled Trees’,’Philosophical Studies 29, 149–168.Google Scholar
  4. Priest, G. (1979), ‘Logic of Paradox’,Journal of Philosophical Logic 8, 219–241.Google Scholar
  5. Priest, G. and R. Sylvan (1992), ‘Simplified Semantics for Basic Relevant Logics’,Journal of Philosophical Logic 21, 217–232.Google Scholar
  6. Restall, G. (1993), ‘Simplified Semantics for Relevant Logics (and Some of Their Rivals)’,Journal of Philosophical Logic 22, 481–511.Google Scholar
  7. Routley, R., V. Plumwood, R. Meyer and R. Brady (1982),Relevant Logics and their Rivals, Ridgeview.Google Scholar
  8. Slaney, J. (1990), ‘A General Logic’,Australian Journal of Philosophy 68, 74–88.Google Scholar
  9. Slaney, J. (1989), ‘Finite Models for some Non-Classical Logics’, Technical Report TR-ARP-2/90, Automated Reasoning Project, Australian National University, Canberra.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Greg Restall
    • 1
  1. 1.Automated Reasoning ProjectAustralian National UniversityCanberraAustralia

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