The General and Finite Satisfiability Problems for PCTL are Undecidable
arxiv（2024）
摘要
The general/finite PCTL satisfiability problem asks whether a given PCTL
formula has a general/finite model. We show that the finite PCTL satisfiability
problem is undecidable, and the general PCTL satisfiability problem is even
highly undecidable (beyond the arithmetical hierarchy). Consequently, there are
no sound deductive systems proving all generally/finitely valid PCTL formulae.
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