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Journal of Logic and Computation 2002 12(2):243-253; doi:10.1093/logcom/12.2.243
© 2002 by Oxford University Press
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Original Article

Monadic Logic of Order over Naturals has no Finite Base

Danièle Beauquier1 and Alexander Rabinovich2

1 Laboratory of Algorithmics, Complexity and Logic, Department of Informatics, University Paris-12, France. E-mail: beauquier{at}univ-paris12.fr 2 Department of Computer Science, Tel-Aviv University, Israel. E-mail: rabino{at}math.tau.ac.il

A major result concerning Temporal Logics (T L) is Kamp's theorem which states that the temporal logic over the pair of modalities X until Y and X since Y is expressively complete for the first-order fragment of monadic logic of order over the natural numbers. We show that there is no finite set of modalities B such that the temporal logic over B and monadic logic of order have the same expressive power over the natural numbers. As a consequence of our proof, we obtain that there is no finite base temporal logic which is expressively complete for the µ-calculus.

Keywords: Temporal logics; monadic logics

Received September 2000.


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