2025/03/19 by Guillaume Massas, Aguilera, Juan P., Massas, Guillaume
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2503.15292
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following a suggestion of Birkhoff and Von Neumann [Ann. Math. 37 (1936), 23-32], we pursue a joint study of quantum logic and intuitionistic logic. We exhibit a linear-time translation which for each quantum logic Q and each superintuitionistic logic I yields an axiomatization of Q∩ I from axiomatizations of Q and I. The translation is centered around a certain axiom (Ex) which (together with introduction and elimination rules for connectives) is shown to axiomatize the intersection of orthologic and intuitionistic logic, solving a problem of Holliday [Logics 1 (2023), pp. 36-79]. We prove that the lattice of all super-Ex logics is isomorphic to the product of the lattices of quantum logics and superintuitionistic logics in the signature \∧,∨,¬\. We prove that there are infinitely many sub-Ex logics extending Holliday's fundamental logic.