A First-Order Framework for Inquisitive Modal Logic

Silke Meißner; Martin Otto

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arXiv · 1906.04981

A First-Order Framework for Inquisitive Modal Logic

Silke Meißner·Martin Otto

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Abstract

We present a natural standard translation of inquisitive modal logic 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 InqML. This translation is based on a graded notion of flatness that ties the inherent second-order, team-semantic features of 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 InqML. Moreover, we prove a Hennessy-Milner theorem for 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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BibTeX RIS

Silke Meißner, Martin Otto. 2019-06-12. A First-Order Framework for Inquisitive Modal Logic. https://arxiv.org/abs/1906.04981

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