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Connexive implication

Published online by Cambridge University Press:  12 March 2014

Storrs Mccall
Storrs Mccall*
Affiliation:
Makerere University College, Kampala, Uganda
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Extract

This paper contains a rigorous treatment of the species of implication described in [8] and [9], where it was given the name of connexive implication. A brief historical survey will lay bare its roots in antiquity, and it will be shown that none of the well-known systems of propositional logic serves to formalize it.1 In this paper a new system of ‘connexive’ logic will be presented, the system being shown to be (a) consistent, (b) independent of two-valued logic, (c) Post-complete.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 3 , 02 September 1966 , pp. 415 - 433
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Anderson, A. R. and Belnap, N. D. Jr., The pure calculus of entailment, this Journal, vol. 27 (1962), pp. 19–52.Google Scholar
[2]Angell, R. B., A propositional logic with subjunctive conditionals, this Journal, vol. 27 (1962), pp. 327–343.Google Scholar
[3]Belnap, N. D. Jr., and Wallace, J. R., A decision procedure for the system Eī of entailment with negation, Technical report No. 11, Office of Naval Research, New Haven 1961.Google Scholar
[4]Burks, A. W. and Copi, I. M., Lewis Carroll's barbershop paradox, Mind, vol. 59 (1950), pp. 219–222.CrossRefGoogle Scholar
[5]Kneale, William, Aristotle and the Consequentia Mirabilis, Journal of Hellenic Studies 77, part i (1957), pp. 62–66.CrossRefGoogle Scholar
[6]William, and Kneale, Martha, The development of logic, Oxford 1962.Google Scholar
[7]McCall, Storrs, A modal logic with eight modalities, ch. 4 of Logic and philosophy of science, Essays in honor of I. M. Bochenski, Amsterdam 1965.Google Scholar
[8]McCall, Storrs, A new variety of implication (abstract), this Journal, vol. 29 (1964), pp. 151–152.Google Scholar
[9]McCall, Storrs, Non-classical prepositional calculi, doctoral thesis, Oxford University, 1963.Google Scholar
[10]Nelson, E. J., Intensional relations, Mind, vol. 39 (1930), pp. 440–453.CrossRefGoogle Scholar
[11]Prior, A. N., Formal logic, 2nd edition, Oxford 1962.Google Scholar
[12]Słupecki, Jerzy, Der volle dreiwertige Aussagenkalkül, Comptes Rendus de la Société des Sciences et des Lettres de Varsovie, Cl. III, vol. 29 (1936), pp. 9–11. English translation to appear in Polish logic, published by the Clarendon Press.Google Scholar
[13]Strawson, P. F., Introduction to logical theory, London 1952.Google Scholar