Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-13T10:20:13.094Z Has data issue: false hasContentIssue false
  • English
  • Français

A star-free semantics for R

Published online by Cambridge University Press:  12 March 2014

Edwin D. Mares
Edwin D. Mares*
Affiliation:
Philosophy Department, Victoria University of Wellington, Wellington, New Zealand, E-mail: Edwin.Mares@vuw.ac.nz
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to show that semantics for relevance logic, based on the Routley-Meyer semantics, can be given without using the Routley star operator to treat negation. In the resulting semantics, negation is treated implicationally. It is shown that, by the use of restrictions on the ternary accessibility relation, simplified by the use of some definitions, a semantics can be stipulated over which R is complete.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 2 , June 1995 , pp. 579 - 590
Copyright
Copyright © Association for Symbolic Logic 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Anderson, A. R. and Belnap, N. D. Jr., Entailment: the logic of relevance and necessity, Vol. 1, Princeton: Princeton University Press, Princeton, New Jersey, 1975.Google Scholar
[2] Anderson, A. R., Belnap, N. D. Jr., and Dunn, J. M., Entailment: the logic of relevance and necessity, Vol. 2, Princeton University Press, Princeton, New Jersey, 1992.Google Scholar
[3] Copeland, B. J., On when a semantics is not a semantics: some reasons for disliking the Routley-Meyer semantics for relevance logic, Journal of Philosophical Logic, vol. 8, (1978), pp. 399–413.Google Scholar
[4] Dunn, J. M., Intuitive semantics for first degree entailment and “coupled trees”, Philosophical Studies, vol. 29, (1976), pp. 149–168.CrossRefGoogle Scholar
[5] Dunn, J. M., Relevance logic and entailment, in Gabbay, D. and Guenther, F. (editors), Handbook of philosophical logic, Vol. 3, Reidel, Dordrecht, 1986, pp. 117–229.CrossRefGoogle Scholar
[6] Meyer, R. K., Metacompleteness, Notre Dame Journal of Formal Logic, vol. 17, (1976), pp. 501–516.CrossRefGoogle Scholar
[7] Routley, R., The American plan completed: alternative classical-style semantics, without stars, for relevant and paraconsistent logics, Studia Logica, vol. 43, (1984), pp. 327–376.CrossRefGoogle Scholar
[8] Routley, R. and Meyer, R. K., The semantics of entailment, II, Journal of Philosophical Logic, vol. 1, (1972), pp. 53–73.CrossRefGoogle Scholar
[9] Routley, R. and Meyer, R. K., The semantics of entailment. I, in Leblanc, H. (editor), Truth, syntax and modality, North-Holland, Amsterdam, 1973, pp. 199–243.CrossRefGoogle Scholar
[10] Routley, R. and Routley, V., Semantics of first degree entailment, Noûs, vol. 6, (1972), pp. 335–359.CrossRefGoogle Scholar