Future temporal logic needs infinitely many modalities

  • Authors:
  • Yoram Hirshfeld;Alexander Rabinovich

  • Affiliations:
  • School of Mathematics, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel;School of Computer Science, The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

  • Venue:
  • Information and Computation
  • Year:
  • 2003

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Abstract

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).