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A star-free semantics for R

  • Edwin D. Mares (a1)

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.

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[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.
[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.
[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. 399413.
[4] Dunn, J. M., Intuitive semantics for first degree entailment and “coupled trees”, Philosophical Studies, vol. 29, (1976), pp. 149168.
[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. 117229.
[6] Meyer, R. K., Metacompleteness, Notre Dame Journal of Formal Logic, vol. 17, (1976), pp. 501516.
[7] Routley, R., The American plan completed: alternative classical-style semantics, without stars, for relevant and paraconsistent logics, Studia Logica, vol. 43, (1984), pp. 327376.
[8] Routley, R. and Meyer, R. K., The semantics of entailment, II, Journal of Philosophical Logic, vol. 1, (1972), pp. 5373.
[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. 199243.
[10] Routley, R. and Routley, V., Semantics of first degree entailment, Noûs, vol. 6, (1972), pp. 335359.

A star-free semantics for R

  • Edwin D. Mares (a1)

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