{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T00:47:19Z","timestamp":1703033239139},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T00:00:00Z","timestamp":1643241600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,12]]},"abstract":"Abstract<\/jats:title>We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product<\/jats:italic> on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural<\/jats:italic> calculus, because some of the standard structural sequent rules are restricted\u2014by lifting all such restrictions, one recovers a calculus for classical logic.<\/jats:p>","DOI":"10.1017\/s1755020322000016","type":"journal-article","created":{"date-parts":[[2022,1,27]],"date-time":"2022-01-27T06:48:20Z","timestamp":1643266100000},"page":"1177-1198","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["A SUBSTRUCTURAL GENTZEN CALCULUS FOR ORTHOMODULAR QUANTUM LOGIC"],"prefix":"10.1017","volume":"16","author":[{"given":"DAVIDE","family":"FAZIO","sequence":"first","affiliation":[]},{"given":"ANTONIO","family":"LEDDA","sequence":"additional","affiliation":[]},{"given":"FRANCESCO","family":"PAOLI","sequence":"additional","affiliation":[]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5509-2980","authenticated-orcid":false,"given":"GAVIN","family":"ST. JOHN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,1,27]]},"reference":[{"key":"S1755020322000016_r27","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31555-8_4"},{"key":"S1755020322000016_r10","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-015-1765-7"},{"key":"S1755020322000016_r23","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9055.001.0001"},{"key":"S1755020322000016_r12","doi-asserted-by":"publisher","DOI":"10.1023\/B:IJTP.0000048815.92983.6e"},{"key":"S1755020322000016_r1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90037-0"},{"key":"S1755020322000016_r17","volume-title":"Residuated Lattices: An Algebraic Glimpse at Substructural Logics","volume":"151","author":"Galatos","year":"2007"},{"key":"S1755020322000016_r16","volume-title":"Abstract Algebraic Logic: An Introductory Textbook","author":"Font","year":"2016"},{"key":"S1755020322000016_r14","volume-title":"Protoalgebraic Logics","author":"Czelakowski","year":"2010"},{"key":"S1755020322000016_r30","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-021-09946-1"},{"key":"S1755020322000016_r7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1201-9_2"},{"key":"S1755020322000016_r2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19800970122"},{"key":"S1755020322000016_r13","first-page":"221","article-title":"A regular sequent calculus for quantum logic in which \n\n\n\n$\\wedge$\n\n\n and \n\n\n\n$\\vee$\n\n\n are dual","volume":"25","author":"Cutland","year":"1982","journal-title":"Logique et Analyse"},{"key":"S1755020322000016_r19","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1245158085"},{"key":"S1755020322000016_r22","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093883401"},{"key":"S1755020322000016_r11","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020313000099"},{"key":"S1755020322000016_r4","doi-asserted-by":"publisher","DOI":"10.1201\/b17294"},{"key":"S1755020322000016_r5","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-8299-z"},{"key":"S1755020322000016_r29","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-3179-9"},{"key":"S1755020322000016_r15","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0526-4"},{"key":"S1755020322000016_r6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196703001511"},{"key":"S1755020322000016_r20","doi-asserted-by":"publisher","DOI":"10.1007\/BF00652069"},{"key":"S1755020322000016_r26","unstructured":"[26] Metcalfe, G. , Paoli, F. , & Tsinakis, C. (2010). Ordered algebras and logic. In Hosni, H. and Montagna, F. , editors. Uncertainty and Rationality, Publications of the Scuola Normale Superiore di Pisa, Pisa, Vol. 10, pp. 1\u201385."},{"key":"S1755020322000016_r9","doi-asserted-by":"publisher","DOI":"10.18514\/MMN.2017.1730"},{"key":"S1755020322000016_r28","doi-asserted-by":"publisher","DOI":"10.2307\/2273194"},{"key":"S1755020322000016_r18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2010.01.003"},{"key":"S1755020322000016_r31","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1154698583"},{"key":"S1755020322000016_r3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-5215-7"},{"key":"S1755020322000016_r24","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19740202504"},{"key":"S1755020322000016_r8","doi-asserted-by":"publisher","DOI":"10.18778\/0138-0680.46.1.2.07"},{"key":"S1755020322000016_r25","unstructured":"[25] Kornell, A. (2021). A\u00a0natural deduction system for orthomodular quantum logic. 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