Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.05383 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909394997870592 |
|---|---|
| author | Kornell, Andre |
| author_facet | Kornell, Andre |
| contents | Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with exactly one semantics for propositional formulas that use negation, conjunction, and implication. In particular, implication must be interpreted as the Sasaki arrow, which satisfies the deduction theorem in this logic. As an application, this deductive system is extended to two systems of predicate logic: the first is sound for Takeuti's quantum set theory, and the second is sound for a variant of Weaver's quantum logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05383 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A natural deduction system for orthomodular logic Kornell, Andre Logic Mathematical Physics Operator Algebras Quantum Physics 03G12 (Primary) 06C15, 03E70, 46L89 (Secondary) Orthomodular logic is a weakening of quantum logic in the sense of Birkhoff and von Neumann. Orthomodular logic is shown to be a nonlinear noncommutative logic. Sequents are given a physically motivated semantics that is consistent with exactly one semantics for propositional formulas that use negation, conjunction, and implication. In particular, implication must be interpreted as the Sasaki arrow, which satisfies the deduction theorem in this logic. As an application, this deductive system is extended to two systems of predicate logic: the first is sound for Takeuti's quantum set theory, and the second is sound for a variant of Weaver's quantum logic. |
| title | A natural deduction system for orthomodular logic |
| topic | Logic Mathematical Physics Operator Algebras Quantum Physics 03G12 (Primary) 06C15, 03E70, 46L89 (Secondary) |
| url | https://arxiv.org/abs/2109.05383 |