Journal of Philosophical Logic

, Volume 28, Issue 4, pp 329–369

The logic of historical necessity as founded on two-dimensional modal tense logic

  • Lennart Åqvist

DOI: 10.1023/A:1004425728816

Cite this article as:
Åqvist, L. Journal of Philosophical Logic (1999) 28: 329. doi:10.1023/A:1004425728816


We consider a version of so called T × W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes the technique of systematic frame constants in order to handle the problem of irreflexivity in tense logics, well known since Gabbay (1981). Axiomatizations are given for two infinite hierarchies of two-dimensional modal tense logics, one without and one with the characteristic operators for historical necessity and possibility. Strong and weak completeness results are obtained for both hierarchies as well as a result to the effect that two approaches to their semantics are equivalent, much in the spirit of Di Maio and Zanardo (1996) and von Kutschera (1997).

historical necessityfinite two-dimensional coordinate systemframe constants

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Lennart Åqvist
    • 1
  1. 1.Institutionen Juridiska FakultetenUppsala Universitet JuridiskaUppsalaSweden