{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T12:18:26Z","timestamp":1754396306559},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6279,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:p>An implication A \u2283 B is said to be null in case A is false in all instances. This note describes several formal systems for first-order predicate logic and arithmetic in which null implications do not occur. In fact, the most restrictive systems avoid the occurrences of any formulas which represent null predicates. The precise sense of this avoidance is explained below.<\/jats:p><jats:p>An intuitionistic negation is a statement of the form A \u2283 F where F is a contradiction. The absence of null implications among true statements entails the absence of intuitionistic negations, and hence systems described here might be called negationless intuitionistic systems.<\/jats:p>","DOI":"10.2307\/2269691","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:36:19Z","timestamp":1146947779000},"page":"562-572","source":"Crossref","is-referenced-by-count":9,"title":["Non-null implication"],"prefix":"10.1017","volume":"31","author":[{"given":"David","family":"Nelson","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200066007_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1947-0025420-1"},{"key":"S0022481200066007_ref003","first-page":"1127","article-title":"Negationless intuitionistic mathematics. I","volume":"49","author":"Griss","year":"1946","journal-title":"Koninklijke Nederlandsche Akademie van Wetenschappen, Proceedings of the section of sciences"},{"key":"S0022481200066007_ref002","unstructured":"Gilmore P. C. , The effect of Griss' criticism of the intuitionistic logic on deductive theories formalized within the intuitionistic logic (Dissertation, Amsterdam, 1953), Amsterdam; also Koninklijke Nederlandsche Akademie van Wetenschappen, Proceedings of the section of sciences , vol. 56 (1953), pp. 162\u2013174; 175\u2013186."},{"key":"S0022481200066007_ref001","first-page":"112","article-title":"Zur intuitionistischen Deutung logischer Formeln","volume":"4","author":"Freudenthal","year":"1937","journal-title":"Compositio mathematica"},{"key":"S0022481200066007_ref004","volume-title":"Intuitionism. An introduction","author":"Heyting","year":"1956"},{"key":"S0022481200066007_ref005","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200066007_ref008","first-page":"91","article-title":"Review of [2]","volume":"21","author":"Nelson","year":"1956","journal-title":"this Journal"},{"key":"S0022481200066007_ref009","volume-title":"Acta Philosophica Fennica","author":"Valpola","year":"1955"},{"key":"S0022481200066007_ref010","first-page":"204","article-title":"The logic of negationless mathematics","volume":"11","author":"Vredenduin","year":"1953","journal-title":"Compositio mathematica"},{"key":"S0022481200066007_ref006","first-page":"285","volume-title":"Constructivity in mathematics","author":"Kleene","year":"1959"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200066007","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:40:13Z","timestamp":1557690013000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200066007\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1966,12]]}},"alternative-id":["S0022481200066007"],"URL":"https:\/\/doi.org\/10.2307\/2269691","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}