On Gabbay's Temporal Xed Point Operator
نویسنده
چکیده
We discuss the temporal logic`USF', involving Until, Since and the xed point operator ' of Gabbay, with semantics over the natural numbers. We show that any formula not involving Until is equivalent to one without nested xed point operators. We then prove that USF has expressive power matching that of the monadic second-order logic S1S. The proof shows that any USF-formula is equivalent to one with at most two nested xed point operators | i.e., no branch of its formation tree has more than two ''s. We then axiomatise USF and prove that it is decidable, with PSPACE-complete satissability problem. Finally, we discuss an application of these results to the executable temporal logic system`MetateM'.
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