Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic

Jim de Groot; João Marcos; Rodrigo Stefanes

doi:10.4204/eptcs.447.26

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arXiv · 2606.31879

Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic

Jim de Groot·João Marcos·Rodrigo Stefanes

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Abstract

We define the notion of IK-bisimulation between the relational semantics for the intuitionistic modal logic IK, and prove that IK arises as the IK-bisimulation-invariant fragment of intuitionistic first-order logic. En route, we provide an intrinsic characterisation result of this logic by way of a Hennessy-Milner-style theorem and develop some intuitionistic first-order model theory, including intuitionistic analogues of Los's Theorem, elementary embeddings and countable saturation.

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Jim de Groot, João Marcos, Rodrigo Stefanes. 2026-06-30. Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic. https://doi.org/10.4204/eptcs.447.26

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