The General and Finite Satisfiability Problems for PCTL are Undecidable
<|reference_start|>The General and Finite Satisfiability Problems for PCTL are Undecidable: 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.<|reference_end|>
@article{chodil2024the,
    title={The General and Finite Satisfiability Problems for PCTL are Undecidable},
    author={Miroslav Chodil and Anton'in Kuv{c}era},
    journal={arXiv preprint arXiv:2404.10648},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.10648},
    primaryClass={cs.LO}
}