The Modal Logics of the Poison Game

Blando, Francesca Zaffora; Mierzewski, Krzysztof; Areces, Carlos

doi:10.1007/978-981-15-2221-5_1

Cited by 6 publications

(1 citation statement)

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“…In particular, one can replace the universal modality by an extra standard modality that can survey the domain by employing the well-known ‘spypoint technique’ from hybrid logic. A detailed syntactic construction of this sort for modal logics of graph games can be found in Zaffora Blando, Mierzewski, & Areces, 2020.…”

Section: Complexity and Undecidabilitymentioning

confidence: 99%

The Modal Logic of Stepwise Removal

Benthem

Mierzewski²,

Blando³

2020

The Review of Symbolic Logic

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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 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.

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Section: Complexity and Undecidabilitymentioning

confidence: 99%