Skip to main content
Log in

The deducibilities of S5

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Anderson, A. R. and Belnap, N. D., Entailment, vol. 1, Princeton University Press, 1975.

  • Carnap, R., ‘Modalities and quantification’, The Journal of Symbolic Logic 11 (1946), 33–64.

    Google Scholar 

  • Feys, R., ‘Les systèmes formalisés des modalités aristotéliciennes’, Revue Philosophique de Louvain 48 (1950), 478–509.

    Google Scholar 

  • Gentzen, G., ‘Untersuchungen über das logische Schliessen’, Mathematische Zeitschrift 39 (1934), 176–210 and 405–431.

    Google Scholar 

  • Gödel, K., ‘Eine Interpretation des intuitionistischen Aussagenkalküls’, Ergebnisse eines mathematischen Kolloquiums 4 (1932), 39–40.

    Google Scholar 

  • Harrop, R., ‘On the existence of finite models and decision procedures for propositional calculi’, Proceedings of the Cambridge Philosophical Society 54 (1958), 1–13.

    Google Scholar 

  • Hiź, H., ‘Complete sentential calculi admitting extensions’, Summer Institute of Symbolic Logic in 1957 at Cornell University, 2, 260–262.

  • Hiź, H., ‘Extendible sentential calculus’, The Journal of Symbolic Logic 24 (1959). 193–202.

    Google Scholar 

  • Lambros, C. H., ‘A generalized theorem concerning a restricted rule of substitution in the field of propositional calculi’, Notre Dame Journal of Formal Logic 20 (1979), 760–764.

    Google Scholar 

  • Lemmon, E. J., ‘Algebraic semantics for modal logics, II’, The Journal of Symbolic Logic 31 (1966), 191–218.

    Google Scholar 

  • Lemmon, E. J., in collaboration with D. S. Scott, An Introduction to Modal Logic (ed. K. Segerberg), Basil Blackwell, Oxford, 1977.

    Google Scholar 

  • Lemmon, E. J., Meredith, C. A., Meredith, D., Prior, A. N. and Thomas, I., Calculi of Pure Strict Implication, Christchurch, 1957.

  • Lewis, C. I. and Langford, C. H., Symbolic Logic, New York, 1932, (reprint Dover, 1959).

  • Łoś, J. and Suszko, R., ‘Remarks on sentential logics’, Koninklijke Nederlandse Akademie van Wetenschappen, ser. A 61 (1958), 177–183.

    Google Scholar 

  • McKinsey, J. C. C. and Tarski, A., ‘Some theorems about the sentencial calculi of Lewis and Heyting’, The Journal of Symbolic Logic 13 (1948) 1–15.

    Google Scholar 

  • Moh Shaw-Kwei, ‘The deduction theorem and two new logical systems’, Methodos 2 (1950), 56–75.

    Google Scholar 

  • Pogorzelski, W. A., ‘On the scope of the classical deduction theorem’, The Journal of Symbolic Logic 33 (1968), 77–81.

    Google Scholar 

  • Pogorzelski, W. A., ‘Structural completeness of the propositional calculus’, Bulletin de l'Académe Polonaise des Sciences, ser. math. 19 (1971), 349–351.

    Google Scholar 

  • Porte, J., ‘Un système pour le calcul des propositions où la règle de détachement n'est pas valable’, Comptes-Rendus de l'Académie des Sciences de Paris 251 (1960), 188–189.

    Google Scholar 

  • Porte, J., ‘Quelques extensions du théorème de déduction’, Revista de la Unión Matemática Argentina 20 (1960, published 1961), 259–266.

    Google Scholar 

  • Porte, J., ‘Un système logistique très faible pour le calcul propositionnel classique’, Comptes-Rendus de l'Académie des Sciences de Paris 254 (1962), 2500–2502.

    Google Scholar 

  • Porte, J., Recherches sur la théorie générale des systèmes formels, Gauthier-Villars, Paris and Nauwelaerts, Leuven, 1965.

    Google Scholar 

  • Prucnal, T., ‘Structural completeness of Lewis's system S5’, Bulletin de l'Académie Polonaise des Sciences, ser. math. 20 (1972), 101–103.

    Google Scholar 

  • Scroggs, S. J., ‘Extensions of the Lewis system S5’, The Journal of Symbolic Logic 16 (1951), 112–120.

    Google Scholar 

  • Słupecki, J., ‘Über die Regeln des Aussagenkalküls’, Studia Logica 1 (1953), 19–40.

    Google Scholar 

  • Smiley, T., ‘The independence of connectives’, The Journal of Symbolic Logic 27 (1962), 426–436.

    Google Scholar 

  • Surma, S. J., ‘The deduction theorems valid in certain fragments of the Lewis' system S2 and the system T of Feys-von Wright’, Studia Logica 31 (1972), 127–136.

    Google Scholar 

  • Wajsberg, M., ‘Ein erweiterter Klassenkalkül’, Monatshefte für Mathematik und Physik 40 (1933), 113–126.

    Google Scholar 

  • Wang, H., ‘Note on the rules of inference’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 11 (1965), 193–196.

    Google Scholar 

  • Zarnecka-Bialy, E., ‘A note on deduction theorem for Gödel's propositional calculus G4*’, Studia Logica 23 (1968) 35–40.

    Google Scholar 

  • Zeman, J. J., Modal Logic, The Clarendon Press, Oxford, 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Porte, J. The deducibilities of S5. J Philos Logic 10, 409–422 (1981). https://doi.org/10.1007/BF00248735

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00248735

Navigation