The closed fragment of IL is PSPACE hard

Félix Bou; Joost J. Joosten

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arXiv · 2004.06398

The closed fragment of IL is PSPACE hard

Félix Bou·Joost J. Joosten

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Abstract

In this paper from 2011 we consider $\textbf{IL}_0$, the closed fragment of the basic interpretability logic $\textbf{IL}$. We show that we can translate $\textbf{GL}_1$, the one variable fragment of G\"odel-L\"ob's provabilty logic $\textbf{GL}$, into $\textbf{IL}_0$. Invoking a result on the PSPACE completeness of $\textbf{GL}_1$ we obtain the PSPACE hardness of $\textbf{IL}_0$.

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BibTeX RIS

Félix Bou, Joost J. Joosten. 2020-04-14. The closed fragment of IL is PSPACE hard. https://arxiv.org/abs/2004.06398

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