Year: 2026
Type: article
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 a → b := ¬a ∨ (a ∧ b).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 iExlogic with modal operators.
DOI: 10.4204/eptcs.447.2
Authors: Juan P. Aguilera, Guillaume Massas
Institutions: TU Wien, Chapman University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Austrian Science Fund
OpenAlex ID: W7166464024