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arXiv · 2103.05117

The Modal Logic of Stepwise Removal

Johan van Benthem·Krzysztof Mierzewski·Francesca Zaffora Blando
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Abstract

We investigate the modal logic of stepwise removal of objects, both for its intrinsic interest as a logic of quantification without replacement, and as a pilot study to better understand the complexity jumps between dynamic epistemic logics of model transformations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic ($\textsf{MLSR}$) and its corresponding removal modality, we analyze its expressive power and prove a bisimulation characterization theorem. We then provide a complete Hilbert-style axiomatization for the logic of stepwise removal in a hybrid language enriched with nominals and public announcement operators. Next, we show that model-checking for $\textsf{MLSR}$ is PSPACE-complete, while its satisfiability problem is undecidable. Lastly, we consider an issue of fine-structure: the expressive power gained by adding the stepwise removal modality to fragments of first-order logic.

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Johan van Benthem, Krzysztof Mierzewski, Francesca Zaffora Blando. 2021-03-08. The Modal Logic of Stepwise Removal. https://doi.org/10.1017/s1755020320000258

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