Temporal logics with incommensurable distances are undecidable

Alexander Rabinovich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Temporal logic based on the two modalities "Since" and "Until" (TL) is the most popular logic for the specification of reactive systems. It is often called the linear time temporal logic. However, metric properties of real time cannot be expressed in this logic. The simplest modalities with metric properties are "Xwill happen within δ units of time". The extension of TL by all these modalities with rational S is decidable. We show that the extension of the linear time temporal logic by two modalities "Xwill happen within one unit of time", "X will happen within τ unit of time" is undecidable, whenever τ is irrational.

Original languageEnglish
Pages (from-to)707-715
Number of pages9
JournalInformation and Computation
Issue number5
StatePublished - May 2007


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