{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T07:26:36Z","timestamp":1781335596721,"version":"3.54.1"},"reference-count":20,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,12,1]],"date-time":"2009-12-01T00:00:00Z","timestamp":1259625600000},"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":[[2009,12]]},"abstract":"<jats:p>The Aristotelian syllogistic cannot account for the validity of certain inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether<jats:italic>reductio ad absurdum<\/jats:italic>is needed. Thus our main goal is to derive results on the existence (or nonexistence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments.<\/jats:p>","DOI":"10.1017\/s1755020309990086","type":"journal-article","created":{"date-parts":[[2009,12,10]],"date-time":"2009-12-10T15:23:32Z","timestamp":1260458612000},"page":"647-683","source":"Crossref","is-referenced-by-count":45,"title":["LOGICS FOR THE RELATIONAL SYLLOGISTIC"],"prefix":"10.1017","volume":"2","author":[{"given":"IAN","family":"PRATT-HARTMANN","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"LAWRENCE S.","family":"MOSS","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,12,1]]},"reference":[{"key":"S1755020309990086_ref14","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1515\/9783110211788.143","volume-title":"Logics for Linguistic Structures","author":"Moss","year":"2008"},{"key":"S1755020309990086_ref17","doi-asserted-by":"publisher","DOI":"10.1023\/B:JLLI.0000024735.97006.5a"},{"key":"S1755020309990086_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370209"},{"key":"S1755020309990086_ref1","volume-title":"Logic, or, the Art of Thinking (\u201cThe Port-Royal Logic\u201d)","author":"Arnauld","year":"1662"},{"key":"S1755020309990086_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-2047-7"},{"key":"S1755020309990086_ref8","volume-title":"Aristotle\u2019s Syllogistic","author":"\u0141ukasiewicz","year":"1957"},{"key":"S1755020309990086_ref4","first-page":"331","article-title":"On the syllogism, Part IV","volume":"10","author":"De Morgan","year":"1860","journal-title":"Transactions of the Cambridge Philosophical Society"},{"key":"S1755020309990086_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(92)90063-4"},{"key":"S1755020309990086_ref13","unstructured":"Moss L. 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