• README ⤓ .txt 2026-10-22T165042.936 000000000000792
  The logics complete for orthomodular lattices, in which the distributive law fails while the weaker orthomodular law survives. Consequence is preservation of designated values over the lattice of a Hilbert space's closed subspaces, the motivating model.
• Effect Algebras ⤓ .md 2026-08-20T061111.000 000000000047488
  Foulis and Bennett introduced effect algebras (1994) to generalize quantum logic and probability. Abstracts the structure of quantum effects (positive operators ≤ I). Connects quantum mechanics, fuzzy logic, and generalized probability. Part of the "quantum structures" tradition alongside orthomodular lattices.
• Orthologic ⤓ .md 2026-08-20T053422.000 000000000041120
  Goldblatt, "Semantic analysis of orthologic" (1974). Ortholattices — not orthomodular lattices; adding the orthomodular law gives the stronger system OML. Quantum-inspired. Weaker than Boolean. Minimal quantum logic.
• Partial Boolean Algebras ⤓ .md 2026-10-22T085830.000 000000000047608
  Simon Kochen and E. P. Specker, "Logical structures arising in quantum theory" (1965) and "The problem of hidden variables in quantum mechanics" (1967), where the algebra and the theorem named for them appear together. Revived by Abramsky and Barbosa, "The logic of contextuality" (2021), as the natural setting for contextuality.
• Quantum Logic ⤓ .md 2026-08-20T061023.000 000000000044584
  Garrett Birkhoff and John von Neumann proposed quantum logic (1936) based on the lattice structure of closed subspaces in Hilbert space. The distributive law fails for quantum propositions. Developed further by Mackey, Jauch, Piron, and others. Debated whether it's a genuine "logic" or just the algebra of quantum observables.
• Sasaki Hook ⤓ .md 2026-10-22T092948.000 000000000040944
  Usa Sasaki, "Orthocomplemented lattices satisfying the exchange axiom" (1954), where the projection appeared; Finch (1970) and Mittelstaedt (1972) proposed it as the quantum conditional; Gary Hardegree, "The conditional in quantum logic" (1974) and "Material implication in orthomodular (and Boolean) lattices" (1981), gave the argument that it is the one. Herman, Marsden, and Piziak (1975) classified the alternatives.
• CRITERIA ⤓ .txt 2026-10-22T165042.936 000000000000808
  Not sufficient: Distributive many-valued matrices (Many-Valued). A modal operator formalizing quantum measurement or information over a classical base (Modal, or Applications/Quantum for the computational systems). A quantum programming or Hoare logic, which reasons about quantum programs rather than in the orthomodular propositional calculus (Applications/Quantum).