{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T06:25:59Z","timestamp":1775975159067,"version":"3.50.1"},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":10968,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1984,3]]},"abstract":"<jats:p>In 1949 Nelson [5] proposed a constructive logic in which falsity is conceived in a fashion analogous to that for intuitionistic truth. The predicate calculus <jats:italic>N<\/jats:italic> (for strong negation) was characterized by the usual axioms and rules for positive intuitionistic connectives (see Kleene [4, p. 82, la\u20137 and 9\u201312]), with the additional axiom schemata for strong negation: A \u2283 (\u00acA \u2283 B),<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200034083_eqnU1\"\/><\/jats:disp-formula><\/jats:p><jats:p>Nelson's paper showed that <jats:italic>N<\/jats:italic> may be interpreted with concepts for constructive truth (<jats:italic>P<\/jats:italic>-realizability) and falsity (<jats:italic>N<\/jats:italic>-realizability). The paper also gave mappings between the intuitionistic and strong negation systems of arithmetic.<\/jats:p><jats:p>These mappings are easily adapted to pure predicate calculus. One shows that intuitionistic predicate calculus <jats:italic>I<\/jats:italic> is a subsystem of <jats:italic>N<\/jats:italic> by reading the intuitionistic negation of A as A \u2283 <jats:italic>B<\/jats:italic> &amp; \u00acB in <jats:italic>N<\/jats:italic>. It is possible to map <jats:italic>N<\/jats:italic> into a subsystem of <jats:italic>I<\/jats:italic> using the definition of A\u2032 in [5, p. 19] changing only the definition of (\u00acA)\u2032 for atomic A to A \u2283 B &amp; \u00acB.<\/jats:p>","DOI":"10.2307\/2274105","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:07:02Z","timestamp":1146953222000},"page":"231-233","source":"Crossref","is-referenced-by-count":207,"title":["Constructible falsity and inexact predicates"],"prefix":"10.1017","volume":"49","author":[{"given":"Ahmad","family":"Almukdad","sequence":"first","affiliation":[]},{"given":"David","family":"Nelson","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200034083_ref003","volume-title":"Experience and theory","author":"K\u00f6rner","year":"1966"},{"key":"S0022481200034083_ref001","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19740201903"},{"key":"S0022481200034083_ref004","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200034083_ref002","first-page":"421","article-title":"The GUHA method and the three-valued logic","volume":"7","author":"H\u00e1jek","year":"1971","journal-title":"Kybernetika"},{"key":"S0022481200034083_ref006","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19690151602"},{"key":"S0022481200034083_ref005","first-page":"16","volume":"14","author":"Nelson","year":"1949","journal-title":"Constructible falsity"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200034083","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T21:26:29Z","timestamp":1558646789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200034083\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1984,3]]}},"alternative-id":["S0022481200034083"],"URL":"https:\/\/doi.org\/10.2307\/2274105","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,3]]}}}