On Non-local Propositional and Weak Monodic Quantified CTL

In this paper we prove decidability of two kinds of branching time temporal logics. First we show that the non-local version of propositional PCTL∗, in which truth values of atoms may depend on the branch of evaluation, is decidable. Then we use this result to establish decidability of various fragments of quantified PCTL∗, where the next-time operator can be applied only to formulas with at most one free variable, all other temporal operators and path quantifiers are applicable only to sentences, and the first-order constructs follow the pattern of any of several decidable fragments of first-order logic.