PP-2019-27: van Benthem, Johan and Mierzewski, Krzysztof and Zaffora Blando, Francesca (2019) The Modal Logic of Stepwise Removal. [Pre-print] (In Press)
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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 trans- formations and logics of freely chosen graph changes that get registered in a growing memory. After introducing this logic (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. The new method employed here may well work for a wide range of modal logics of graph change. Next, we show that model-checking for 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.
| Item Type: | Pre-print |
|---|---|
| Report Nr: | PP-2019-27 |
| Series Name: | Prepublication (PP) Series |
| Year: | 2019 |
| Additional Information: | This paper will appear in "Reports on Symbolic Logic". |
| Subjects: | Computation Logic |
| Depositing User: | Johan van Benthem |
| Date Deposited: | 23 Nov 2019 20:50 |
| Last Modified: | 05 Sep 2020 14:26 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1723 |
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