Document Type
Conference Proceeding
Publication Date
6-30-2026
Abstract
We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coincides with the intersection of orthologic and the implication-free fragment of intuitionistic logic. In this paper, we add an implication connective to Ex-logic and axiomatize iEx-logic, the intersection of full intuitionistic logic and orthomodular logic with the implication connective interpreted as the Sasaki hook. As a consequence, we obtain a characterization of the lattice of logics extending iEx-logic as the product of the lattice of intermediate logics and the lattice of orthomodular logics. We also explore the robustness of our algebraic approach by briefly discussing extensions of iEx-logic with modal operators.
Recommended Citation
J.P. Aguilera & G. Massas (2026): Conditionals and Modalities in Constructive Quantum Logics. In M. Bílková, M. Gattinger, I. van der Giessen, M. Girlando, and Y. Wang, editors: Advances in Modal Logic, 16, Electronic Proceedings in Theoretical Computer Science (EPTCS). https://doi.org/10.4204/EPTCS.447.2
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Proceedings of the Sixteenth International Conference on Advances in Modal Logic, volume 16, in 2026. https://doi.org/10.4204/EPTCS.447.2