Year: 2025
Type: article
Abstract: Let $\mathsf{QPL}^{\mathrm{e}}$ expand the quantifier-free "polynomial" probability logic of [4] (R. Fagin et al., 1990) by adding quantifiers over arbitrary events; it can be viewed as a one-sorted elementary language for reasoning about probability spaces. We prove that the $\Sigma_2$-fragment of the $\mathsf{QPL}^{\mathrm{e}}$-theory of finite spaces is hereditarily undecidable. By earlier observations, this implies that $\Pi_2$ is the maximal decidable prefix fragment of $\mathsf{QPL}^{\mathrm{e}}$. Moreover, we obtain similar results for two natural one-sorted logics of probability that emerge from [1] (M. Abadi and J. Y. Halpern, 1994).
Source: Izvestiya Mathematics
DOI: 10.4213/im9652e
Author: Stanislav Olegovich Speranski
Institution: Steklov Mathematical Institute
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411206701