Abstract
In the context of temporal logic the word “completeness” is heavily overused, having at least three different meanings: first of all, a flow of time is called (Dedekind-)complete if every set of time points which is bounded to the right has a supremum. Secondly, a set of temporal operators is called functionally, or expressively, complete over a class C of temporal structures, if it has the same expressive power over C as monadic first-order logic. And thirdly, an axiomatization is complete with respect to a class К of flows of time, if it recursively enumerates the set of formulas that are valid in К. In this paper, we will show that in the case of the formalism with S and U, the three notions of completeness are interwoven.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Burgess, John P., Axioms for Tense Logic: I. “Since” and “Until.” Notre Dame Journal of Formal Logic 23 (1982) 367–374.
Doets, Kees., Monadic Hi-Theories of Hi-Properties. Notre Dame Journal of Formal Logic 30 (1989) 224–240.
Gabbay, Dov M., Handbook of Temporal Logic. Forthcoming.
Gabbay, D.M. and I.M. Hodkinson, An axiomatization of the temporal logic with Until and Since over the real numbers. Journal of Logic and Computation 1 (1990) 229–259.
Kamp, J.A.W., Tense Logic and the Theory of Linear Order. Doctoral dissertation, University of California at Los Angeles, 1968.
Venema, Yde, Many-dimensional modal logic. Doctoral dissertation, Universiteit van Amsterdam, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Venema, Y. (1993). Completeness via Completeness. In: de Rijke, M. (eds) Diamonds and Defaults. Synthese Library, vol 229. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8242-1_12
Download citation
DOI: https://doi.org/10.1007/978-94-015-8242-1_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4286-6
Online ISBN: 978-94-015-8242-1
eBook Packages: Springer Book Archive