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arXiv · 2607.18956

Definable Classes of Models and Frames in Bi-intuitionistic Logic

Guillermo Badia·Tomasz Kowalski·Grigory Olkhovikov
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Abstract

The question of the expressive power of a given logical language with Kripke relational semantics has at least two dimensions: (1) what the language can say about frames, and (2) what it can say about models. The Goldblatt-Thomason theorem provides a model-theoretic characterisation of modal axiomatisability for elementary classes of frames in terms of closure under taking generated subframes, disjoint unions, bounded morphic images, and reflection of ultrafilter extensions. Goldblatt also provides a similar characterisation for axiomatisability in intuitionistic logic of classes of models rather than frames. In this article we provide analogous results for bi-intuitionistic logic, a natural expressive extension of intuitionistic logic obtained by adding a binary connective dual to the intuitionistic implication, introduced in the 1970s independently by Dieter Klemke and Cecylia Rauszer. Together with previous results, such as a van Benthem bisimulation characterisation theorem and a Lindstrom theorem, this provides a complete picture of the expressive power of propositional bi-intuitionistic logic.

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Guillermo Badia, Tomasz Kowalski, Grigory Olkhovikov. 2026-07-21. Definable Classes of Models and Frames in Bi-intuitionistic Logic. https://arxiv.org/abs/2607.18956

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