Inquisitive bisimulation

TL;DR

This paper explores inquisitive modal logic (InqML), extending standard epistemic logic to include questions, and characterizes its expressiveness and bisimulation invariance using advanced model-theoretic techniques.

Contribution

It introduces a notion of bisimulation for InqML and characterizes its expressiveness as the bisimulation-invariant fragment of first-order logic over two-sorted structures.

Findings

InqML can be characterized by bisimulation invariance.

InqML extends epistemic logic to include questions.

The paper develops non-classical methods for analyzing non-elementary classes.

Abstract

Inquisitive modal logic InqML is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states. We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. These results crucially require non-classical methods in studying bisimulation and first-order expressiveness over non-elementary classes of structures, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory.