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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