{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T22:13:15Z","timestamp":1648851195512},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":18455,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1963,9]]},"abstract":"<jats:p>Recent interest in \u0141ukasiewicz' L<jats:sub>\u21350<\/jats:sub>, raises the question whether this axiomatic system can be simplified [2]. It is known that \u0141ukasiewicz' fourth axiom CCCPQCQPCQP is dependent [4] p. 51. The axiomatic system resulting from deleting the fourth axiom from L<jats:sub>\u21350<\/jats:sub> will be shown to be \u201cminimal\u201d in the sense that the axioms and rules of inference are mutually independent; consequently, no further simplification of L<jats:sub>\u21350<\/jats:sub>, is possible. By switching basic operators, however, simplified modifications of L<jats:sub>\u21350<\/jats:sub>, can be constructed.<\/jats:p>","DOI":"10.2307\/2271067","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:21:59Z","timestamp":1146932519000},"page":"217-221","source":"Crossref","is-referenced-by-count":1,"title":["Independent Axioms for Infinite-Valued Logic"],"prefix":"10.1017","volume":"28","author":[{"given":"Atwell R.","family":"Turquette","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200117955_ref004","volume-title":"Logic, semantics, metamathematics","author":"Tarski","year":"1956"},{"key":"S0022481200117955_ref003","volume-title":"Many-valued logics","author":"Rosser","year":"1952"},{"key":"S0022481200117955_ref002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1958-0094299-1","article-title":"Fragments of many-valued statement calculi","volume":"87","author":"Rosser","year":"1958","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200117955_ref001","first-page":"111","article-title":"A system of modal logic","volume":"1","author":"\u0141ukasiewicz","year":"1953","journal-title":"The journal of computing systems"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200117955","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T15:16:03Z","timestamp":1559661363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200117955\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1963,9]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1963,9]]}},"alternative-id":["S0022481200117955"],"URL":"https:\/\/doi.org\/10.2307\/2271067","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1963,9]]}}}