Arity hierarchy for temporal logics

Alexander Rabinovich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


A major result concerning temporal logics is Kamp's Theorem which states that the pair of modalities "until" and "since" is expressively complete for the first-order fragment of the monadic logic over the linear-time canonical model of naturals. The paper concerns the expressive power of temporal logics over trees. The main result states that in contrast to Kamp's Theorem, for every n there is a modality of arity n definable by a monadic logic formula, which is not equivalent over trees to any temporal logic formula which uses modalities of arity less than n. Its proof takes advantage of an instance of Shelah's composition theorem.This result has interesting corollaries, for instance reproving that C T L* and E C T L+ have no finite basis.

Original languageEnglish
Pages (from-to)373-381
Number of pages9
JournalTheoretical Computer Science
Issue number2-3
StatePublished - 28 Aug 2008


  • Expressive power
  • Temporal logic


Dive into the research topics of 'Arity hierarchy for temporal logics'. Together they form a unique fingerprint.

Cite this