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THE MODAL LOGIC OF STEPWISE REMOVAL

Part of: General logic

Published online by Cambridge University Press:  21 July 2020

JOHAN VAN BENTHEM ,
KRZYSZTOF MIERZEWSKI  and
FRANCESCA ZAFFORA BLANDO
JOHAN VAN BENTHEM
Affiliation:
STANFORD UNIVERSITY AND LOGICAL DYNAMICS LAB, CSLI STANFORD, CA, USA and ILLC, UNIVERSITY OF AMSTERDAM AMSTERDAM, NETHERLANDS and TSINGHUA UNIVERSITY BEIJING, CHINA E-mail:j.vanbenthem@uva.nl STANFORD UNIVERSITY AND LOGICAL DYNAMICS LAB, CSLI STANFORD, CA, USAE-mail:kmierzew@stanford.eduE-mail:fzaffora@stanford.edu
KRZYSZTOF MIERZEWSKI
Affiliation:
STANFORD UNIVERSITY AND LOGICAL DYNAMICS LAB, CSLI STANFORD, CA, USA and ILLC, UNIVERSITY OF AMSTERDAM AMSTERDAM, NETHERLANDS and TSINGHUA UNIVERSITY BEIJING, CHINA E-mail:j.vanbenthem@uva.nl
FRANCESCA ZAFFORA BLANDO
Affiliation:
STANFORD UNIVERSITY AND LOGICAL DYNAMICS LAB, CSLI STANFORD, CA, USAE-mail:kmierzew@stanford.eduE-mail:fzaffora@stanford.edu
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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 (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 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.

Keywords

dynamic logicshybrid logiclogics for graph gamescomplexity and decidability

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03B42: Logics of knowledge and belief (including belief change)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 1 , March 2022 , pp. 36 - 63
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Copyright
© 2020, Association for Symbolic Logic

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