README⤓ .txt 2026-07-17T152206.000 000000000008936 Logics and calculi individuated by quantum structure: systems whose connectives, states, or processes reflect the non-classical algebra of quantum mechanics—non-distributive lattices of propositions, effect algebras, and the diagrammatic calculi of quantum information. The domain is what unifies them and it is close to the only thing that does: the propositional strand descends from Birkhoff and von Neumann's observation (1936) that the closed subspaces of a Hilbert space fail distribution, since the span of two subspaces contains vectors lying in neither, while the process strand descends from the categorical reconstruction of quantum mechanics in the 2000s, and the two share their subject rather than their machinery.
Effect Algebras⤓ .md 2026-07-15T055427.000 000000000025696 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.
Partial Boolean Algebras⤓ .md 2026-07-17T121634.146 000000000000928 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 Computation Logic⤓ .md 2026-07-15T060458.000 000000000021408 Emerged from quantum computing semantics (1990s-2000s). Selinger's QPL (2004). Abramsky and Coecke's categorical quantum mechanics. ZX-calculus (Coecke & Duncan, 2008). Quantum lambda calculi. Bridges quantum physics and programming language theory.
Quantum Hoare Logic⤓ .md 2026-07-15T074454.000 000000000016320 Ying (2011). Program logic for quantum. Partial correctness. Density matrices as states. Foundation for quantum program verification.
Quantum Information Logic⤓ .md 2026-07-17T120407.600 000000000000920 Coecke and others (2000s). Logic for quantum information flow. Entanglement and measurement. Categorical quantum mechanics. Types for quantum protocols.
Quantum Modal Logic⤓ .md 2026-07-15T062344.000 000000000019464 Various approaches combining modal logic and quantum mechanics (2000s-present). Baltag, Smets, Dishkant, Goldblatt. Modal interpretation of quantum observables. Reasoning about quantum measurements and information. Foundation for quantum epistemics.
Quantum Process Theories⤓ .md 2026-07-15T072405.000 000000000013712 Abramsky and Coecke (2004). Categorical quantum mechanics. Processes as morphisms. Dagger compact categories. Foundation for quantum protocols.
Quantum Programming Logic⤓ .md 2026-07-15T063455.000 000000000018456 D'Hondt and Panangaden (2006), Ying (2012). Hoare-style logic for quantum programs. Quantum weakest precondition. Verification of quantum algorithms. Foundation for quantum program correctness.
Quantum Temporal Logic⤓ .md 2026-07-15T061756.000 000000000020024 Emerging area combining temporal logic with quantum systems (2010s-present). Baltazar, Chadha, Mateus, Sernadas and others. Verifying quantum protocols over time. Quantum Markov chains with temporal specifications. Connection to quantum model checking.
Sasaki Hook⤓ .md 2026-07-17T121634.146 000000000000808 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" (1975) and "Material implication in orthomodular lattices" (1979), gave the argument that it is the one. Herman, Marsden, and Piziak (1975) classified the alternatives.
ZX Calculus⤓ .md 2026-07-15T065316.000 000000000015160 Coecke and Duncan (2008). Graphical language for quantum computing. String diagrams for linear maps. Completeness for Clifford+T. Foundation for quantum circuit optimization.
CRITERIA⤓ .txt 2026-07-15T204656.000 000000000008184 Not sufficient: A classical logic merely applied to a physical example. Generic many-valued semantics without quantum structure (Algebraic/Many-Valued).