{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T07:42:54Z","timestamp":1693726974480},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T00:00:00Z","timestamp":1528156800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: All<jats:italic>x<\/jats:italic>are<jats:italic>y<\/jats:italic>and Some<jats:italic>x<\/jats:italic>are<jats:italic>y<\/jats:italic>, There are at least as many<jats:italic>x<\/jats:italic>as<jats:italic>y<\/jats:italic>, and There are more<jats:italic>x<\/jats:italic>than<jats:italic>y<\/jats:italic>. Here<jats:italic>x<\/jats:italic>and<jats:italic>y<\/jats:italic>range over subsets (not elements) of a given<jats:italic>infinite<\/jats:italic>set. Moreover,<jats:italic>x<\/jats:italic>and<jats:italic>y<\/jats:italic>may appear complemented (i.e., as<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1755020318000126_inline1\" \/><jats:tex-math>$\\bar{x}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1755020318000126_inline2\" \/><jats:tex-math>$\\bar{y}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a soundness\/completeness theorem. There are efficient algorithms for proof search and model construction.<\/jats:p>","DOI":"10.1017\/s1755020318000126","type":"journal-article","created":{"date-parts":[[2018,6,5]],"date-time":"2018-06-05T13:27:45Z","timestamp":1528205265000},"page":"1-22","source":"Crossref","is-referenced-by-count":3,"title":["SYLLOGISTIC LOGIC WITH CARDINALITY COMPARISONS, ON INFINITE SETS"],"prefix":"10.1017","volume":"13","author":[{"given":"LAWRENCE S.","family":"MOSS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SEL\u00c7UK","family":"TOPAL","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2018,6,5]]},"reference":[{"key":"S1755020318000126_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-29300-4_18"},{"key":"S1755020318000126_ref1","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1515\/9783110211788.143","volume-title":"Logics for Linguistic Structures","author":"Moss","year":"2008"},{"key":"S1755020318000126_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020309990086"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020318000126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T00:17:54Z","timestamp":1693700274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020318000126\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,5]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2020,3]]}},"alternative-id":["S1755020318000126"],"URL":"https:\/\/doi.org\/10.1017\/s1755020318000126","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,5]]}}}