An axiomatization of PCTL*

  • Authors:
  • Mark Reynolds

  • Affiliations:
  • School of Computer Science and Software Engineering, The University of Western Australia, Perth, Australia

  • Venue:
  • Information and Computation
  • Year:
  • 2005

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Abstract

A sound and complete axiomatization for a computation tree logic with past operators, PCTL*, is given. The logic extends the standard branching time logic CTL* of R-generable models via the use of past time operators and semantics based on a finite linear past leading back from any point in any fullpath. Furthermore, the valid formulas of CTL* are also valid in PCTL*. The past operators allow us to avoid use of any unusual rules of inference such as the ugly automata-motivated AA rule which is part of the existing complete axiomatization for CTL*.