Future temporal logic needs infinitely many modalities

Kamp’s theorem states that there is a temporal logic with two modalities (“until” and “since”) which is expressively complete for the first-order monadic logic of order over the real line. In this paper we show that there is no temporal logic with finitely many modalities which is expressively compl...

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Bibliographic Details
Published in:Information and computation 2003-12, Vol.187 (2), p.196-208
Main Authors: Hirshfeld, Yoram, Rabinovich, Alexander
Format: Article
Language:English
Subjects:
Exact sciences and technology
General logic
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Sciences and techniques of general use
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Summary:Kamp’s theorem states that there is a temporal logic with two modalities (“until” and “since”) which is expressively complete for the first-order monadic logic of order over the real line. In this paper we show that there is no temporal logic with finitely many modalities which is expressively complete for the future fragment of first-order monadic logic of order over the real line (a future formula over the real time line is a formula whose truth value at a point is independent of what happened in the past).
ISSN:0890-5401
1090-2651
DOI:10.1016/S0890-5401(03)00163-9