Projection-algebras and quantum logic

• URL: http://arxiv.org/abs/2402.07042v1
• Date: Sat, 10 Feb 2024 20:52:50 GMT
• Title: Projection-algebras and quantum logic
• Authors: Daniel Lehmann
• Abstract summary: P-algebras are a non-commutative, non-associative generalization of Boolean algebras. A substructural logic of sequents is proved to be sound and complete for the logic of P-algebras.
• Score: 1.930852251165745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: P-algebras are a non-commutative, non-associative generalization of Boolean algebras that are for Quantum Logic what Boolean algebras are for Classical Logic.The closed subspaces of a separable Hilbert space form a P-algebra under orthogonal complementation and projection of a subspace onto another one. P-algebras are complemented orthomodular posets that are not lattices. Atomic algebras are defined and their main properties are studied. A substructural logic of sequents is proved to be sound and complete for the logic of P-algebras.

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