Complete proof system for QPTL

Yonit Kesten, Amir Pnueli

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The paper presents an axiomatic system for quantified propositional temporal logic (QPTL), which is propositional temporal logic equipped with quantification over propositions (Boolean variables). The advantages of this extended temporal logic is that its expressive power is strictly higher than that of the unquantified version (PTL) and is equal to that of S1S, as well as that of ω-automata. Another important application of QPTL is its use for formulating and verifying refinement relations between reactive systems. In fact, the completeness proof is based on the reduction of a QPTL formula into a Büchi automaton, and performing equivalence transformations on this automaton, formally justifying these transformations as a bi-directional refinement.

Original languageEnglish
Pages (from-to)701-745
Number of pages45
JournalJournal of Logic and Computation
Issue number5
StatePublished - 1 Oct 2002


  • Axiomatic system
  • Büchi automata
  • Completeness
  • Flexible variables
  • History scheme
  • Prophesy scheme
  • Refinement
  • Rigid variable
  • Temporal logic


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