{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T15:46:45Z","timestamp":1781279205570,"version":"3.54.1"},"reference-count":15,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2018,11,8]],"date-time":"2018-11-08T00:00:00Z","timestamp":1541635200000},"content-version":"vor","delay-in-days":7,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,11]]},"abstract":"Abstract<\/jats:title>In this study, some conservative extensions of paraconsistent quantum logic, such as Nelsonian, modal, infinitary and temporal, are investigated by extending a single\u2010antecedent\/succedent sequent calculus for paraconsistent quantum logic. A sequent calculus , which is obtained from by adding implication and co\u2010implication, is introduced as a variant of Nelson's paraconsistent four\u2010valued logic. Sequent calculi , and are introduced, respectively, as modal, infinitary and temporal extensions of . The cut\u2010elimination and duality theorems for these calculi are proved, and some extended calculi including and , as well as their fragments, are shown to be decidable. A theorem for embedding into its negation\u2010free fragment and a theorem for embedding into are proved.<\/jats:p>","DOI":"10.1002\/malq.201700012","type":"journal-article","created":{"date-parts":[[2018,11,8]],"date-time":"2018-11-08T19:33:41Z","timestamp":1541705621000},"page":"371-386","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Extending paraconsistent quantum logic: a single\u2010antecedent\/succedent system approach"],"prefix":"10.1002","volume":"64","author":[{"given":"Norihiro","family":"Kamide","sequence":"first","affiliation":[{"name":"Department of Information and Electronic Engineering, Faculty of Science and Engineering Teikyo University Toyosatodai 1\u20101 Utsunomiya Tochigi 320\u20108551 Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2018,11,8]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274105"},{"key":"e_1_2_7_3_1","first-page":"7","volume-title":"Modern Uses of Multiple\u2010Valued Logic","author":"Belnap N. 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October 31\u2013November 2 1977 (IEEE Computer Society 1977) pp.46\u201357.","DOI":"10.1109\/SFCS.1977.32"},{"key":"e_1_2_7_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-85796-5"},{"key":"e_1_2_7_16_1","first-page":"465","article-title":"A constructive propositional calculus with strong negation (in Russian)","volume":"85","author":"Vorob'ev N. N.","year":"1952","journal-title":"Dokl. Akad. Nauk"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201700012","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/api.wiley.com\/onlinelibrary\/chorus\/v1\/articles\/10.1002%2Fmalq.201700012","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T20:46:36Z","timestamp":1694810796000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201700012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11]]},"references-count":15,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1002\/malq.201700012"],"URL":"https:\/\/doi.org\/10.1002\/malq.201700012","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11]]},"assertion":[{"value":"2017-03-12","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-02-13","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-11-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}