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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\u2019s quantum set theory, and the second is sound for a variant of Weaver\u2019s quantum logic.<\/jats:p>","DOI":"10.1017\/s1755020323000229","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T07:04:36Z","timestamp":1688972676000},"page":"910-949","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["A NATURAL DEDUCTION SYSTEM FOR ORTHOMODULAR LOGIC"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8930-7126","authenticated-orcid":false,"given":"ANDRE","family":"KORNELL","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,7,10]]},"reference":[{"key":"S1755020323000229_r36","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1795-4_25"},{"key":"S1755020323000229_r58","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026461417704"},{"key":"S1755020323000229_r79","first-page":"293","article-title":"Orthocomplemented lattices satisfying the exchange axiom","volume":"17","author":"Sasaki","year":"1954","journal-title":"Journal of Science of the Hiroshima University, Series A"},{"key":"S1755020323000229_r81","first-page":"357","article-title":"Quantum logical calculi and lattice structures","volume":"6","author":"Stachow","year":"1976","journal-title":"Journal of Philosophical Logic"},{"key":"S1755020323000229_r29","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511976971"},{"key":"S1755020323000229_r4","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.bjps\/37.1.83"},{"key":"S1755020323000229_r84","doi-asserted-by":"publisher","DOI":"10.1007\/s10516-021-09614-y"},{"key":"S1755020323000229_r20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01565428"},{"key":"S1755020323000229_r56","doi-asserted-by":"publisher","DOI":"10.1007\/s10773-006-9059-6"},{"key":"S1755020323000229_r34","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093891789"},{"key":"S1755020323000229_r45","unstructured":"[45] Kornell, A. 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