Review of Symbolic Logic:1-23 (forthcoming)

Abstract
We present a natural standard translation of inquisitive modal logic $\mathrm{InqML}$ into first-order logic over the natural two-sorted relational representations of the intended models, which captures the built-in higher-order features of $\mathrm{InqML}$. This translation is based on a graded notion of flatness that ties the inherent second-order, team-semantic features of $\mathrm{InqML}$ over information states to subsets or tuples of bounded size. A natural notion of pseudo-models, which relaxes the non-elementary constraints on the intended models, gives rise to an elementary, purely model-theoretic proof of the compactness property for $\mathrm{InqML}$. Moreover, we prove a Hennessy-Milner theorem for $\mathrm{InqML}$, which crucially uses $\omega $ -saturated pseudo-models and the new standard translation. As corollaries we also obtain van Benthem style characterisation theorems.
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DOI 10.1017/s175502032100037x
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References found in this work BETA

Compositional Semantics for a Language of Imperfect Information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
Inquisitive Logic.Ivano Ciardelli & Floris Roelofsen - 2011 - Journal of Philosophical Logic 40 (1):55-94.
Inquisitive Bisimulation.Ivano Ciardelli & Martin Otto - 2021 - Journal of Symbolic Logic 86 (1):77-109.

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