PP-2019-27: The Modal Logic of Stepwise Removal

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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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
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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