Notre Dame Journal of Formal Logic

A Note on the Logic of Eventual Permanence for Linear Time

Rohan French


In a paper from the 1980s, Byrd claims that the logic of "eventual permanence" for linear time is KD5. In this note we take up Byrd's novel argument for this and, treating the problem as one concerning translational embeddings, show that rather than KD5 the correct logic of "eventual permanence" is KD45

Article information

Notre Dame J. Formal Logic Volume 49, Number 2 (2008), 137-142.

First available in Project Euclid: 15 May 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B44: Temporal logic
Secondary: 14E25: Embeddings

eventual permanence translational embedding tense logic


French, Rohan. A Note on the Logic of Eventual Permanence for Linear Time. Notre Dame J. Formal Logic 49 (2008), no. 2, 137--142. doi:10.1215/00294527-2008-003.

Export citation


  • [1] Byrd, M., "Eventual permanence", Notre Dame Journal of Formal Logic, vol. 21 (1980), pp. 591--601.
  • [2] Humberstone, L., "Weaker-to-stronger translational embeddings in modal logic", pp. 279--97 in Advances in Modal Logic, Vol. 6, edited by G. Governatori, I. M. Hodkinson, and Y. Venema, College Publications, London, 2006.
  • [3] Rescher, N., and A. Urquhart, Temporal Logic, vol. 3 of Library of Exact Philosophy, Springer-Verlag, New York, 1971.
  • [4] Segerberg, K., An Essay in Classical Modal Logic. Vols. 1, 2, 3, vol. 13 of Filosofiska Studier, Filosofiska Föreningen och Filosofiska Institutionen vid Uppsala Universitet, Uppsala, 1971.