Notre Dame Journal of Formal Logic

Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants

Rohan French


We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.

Article information

Notre Dame J. Formal Logic, Volume 53, Number 4 (2012), 549-556.

First available in Project Euclid: 8 November 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}

modal logic post-completeness propositional constants


French, Rohan. Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants. Notre Dame J. Formal Logic 53 (2012), no. 4, 549--556. doi:10.1215/00294527-1722746.

Export citation


  • [1] Anderson, A., “A reduction of deontic logic to alethic modal logic,” Mind, vol. 67 (1958), pp. 100–103.
  • [2] Chellas, B. F., Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.
  • [3] Goguadze, G., C. Piazza, and Y. Venema, “Simulating polyadic modal logics by monadic ones,” Journal of Symbolic Logic, vol. 68 (2003), pp. 419–62.
  • [4] Humberstone, L., “Relative necessity revisited,” Reports on Mathematical Logic, vol. 13 (1981), pp. 33–42.
  • [5] Humberstone, L., “Contra-classical logics,” Australasian Journal of Philosophy, vol. 78 (2000), pp. 438–74.
  • [6] Kohn, R. V., “Some post-complete extensions of S2 and S3,” Notre Dame Journal of Formal Logic, vol. 18 (1977), pp. 467–70.
  • [7] Makinson, D., and K. Segerberg, “Post completeness and ultrafilters,” Mathematical Logic Quarterly, vol. 20 (1974), pp. 385–88.
  • [8] Nowell-Smith, P., and E. Lemmon, “Escapism: The logical basis of ethics,” Mind, vol. 69 (1960), pp. 289–300.
  • [9] Segerberg, K., “Post completeness in modal logic,” Journal of Symbolic Logic, vol. 37 (1972), pp. 711–15.
  • [10] Segerberg, K., “Halldén’s theorem on Post completeness,” pp. 206–9 in Modality, Morality and Other Problems of Sense and Nonsense: Essays Dedicated to Sören Halldén, CWK Gleerup Bokforlag, Lund, 1973.
  • [11] Segerberg, K., “The truth about some Post numbers,” Journal of Symbolic Logic, vol. 41 (1976), pp. 239–44.
  • [12] Williamson, T., “Continuum many maximal consistent normal bimodal logics with inverses,” Notre Dame Journal of Formal Logic, vol. 39 (1998), pp. 128–34.