Monadic logic of order over naturals has no finite base

Danièle Beauquier, Alexander Rabinovich

Research output: Contribution to journalArticlepeer-review

Abstract

A major result concerning Temporal Logics (TL) 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.

Original languageEnglish
Pages (from-to)243-253
Number of pages11
JournalJournal of Logic and Computation
Volume12
Issue number2
DOIs
StatePublished - Apr 2002

Keywords

  • Monadic logics
  • Temporal logics

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