More past glories [temporal logic]

We continue in the same vein as O. Lichtenstein et al. (1985) in "The Glory of the Past", demonstrating the advantages of including past-time operators in using temporal logic in computer science. A normal form for temporal formulas, based on a simple combination of past formulas, is arrived at via syntactic rewrites and is shown to be a useful alternative to automata based temporal reasoning. The use of the normal form in providing a complete axiomatization for PCTL* (i.e. CTL* with past connectives) is sketched.