🤖 AI Summary
This paper precisely characterizes the expressive power of inquisitive modal logic (InqML) over S5-based inquisitive epistemic models. Standard model-theoretic methods fail due to the non-elementary nature of this model class, whose semantics naturally corresponds to two-sorted first-order structures. Method: Leveraging this correspondence, the paper introduces a novel non-classical approach—first representing InqML as the bisimulation-invariant fragment of first-order logic over such two-sorted structures, thereby circumventing limitations of classical model theory. Contribution/Results: It establishes a full expressive completeness result for InqML over natural inquisitive epistemic models, demonstrating an exact correspondence between InqML-definable properties and bisimulation-invariant ones. This yields a rigorous metatheoretic foundation for dynamic epistemic logics involving questions and information dynamics, clarifying the logical boundaries of inquisitive reasoning within standard epistemic frameworks.
📝 Abstract
Inquisitive modal logic, InqML, in its epistemic incarnation, extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. We use the natural notion of bisimulation equivalence in the setting of InqML, as introduced in [Ciardelli/Otto: JSL 2021], to characterise the expressiveness of InqML as the bisimulation invariant fragment of first-order logic over natural classes of two-sorted first-order structures that arise as relational encodings of inquisitive epistemic (S5-like) models. The non-elementary nature of these classes crucially requires non-classical model-theoretic methods for the analysis of first-order expressiveness, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory.
