{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:23:47Z","timestamp":1648567427808},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15990,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1970,6]]},"abstract":"<jats:p>In this paper a number of nonstandard systems of predicate logic with or without identity, are translated with subsystems of applied standard system of predicate logic with identity. There are nonstandard theories of quantification which, following [16], are described as inclusive systems; their theorems are valid in all domains, including the empty domain. Theories of quantification which allow for the substitution of denotationless terms for free variables, are described, following [21], as systems of free logic; they are said to be free of the requirement that all singular terms must have denotations. Free logics and inclusive logics may each be of the other type. A nonstandard theory of identity, described, following [12] as a theory of nonreflexive identity, may be combined with a standard or with a nonstandard theory of quantification. Another kind of nonstandard system of predicate logic examined is a nonstandard version of a system of monadic predicate logic in which a distinction is made between sentence and predicate negation, and which is nonstandard in the sense that the laws relating sentence and predicate negation diverge from the standard ones. In the systems examined, this is combined with an inclusive quantification theory.<\/jats:p>","DOI":"10.2307\/2270518","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:00:41Z","timestamp":1146949241000},"page":"267-294","source":"Crossref","is-referenced-by-count":7,"title":["Nonstandard theories of quantification and identity"],"prefix":"10.1017","volume":"35","author":[{"given":"A.","family":"Trew","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200090939_ref022","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19670131502"},{"key":"S0022481200090939_ref021","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19660120117"},{"key":"S0022481200090939_ref004","first-page":"19","article-title":"Systems of restricted quantification. 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Lambert: Existential import revisited","volume":"4","author":"Church","year":"1963","journal-title":"Notre Dame journal of formal logic"},{"key":"S0022481200090939_ref019","first-page":"181","volume-title":"Bertrand Russell, philosopher of the century","author":"Scott","year":"1967"},{"key":"S0022481200090939_ref013","volume-title":"Logic, methodology and philosophy of science","author":"Mates","year":"1968"},{"key":"S0022481200090939_ref020","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093893527"},{"key":"S0022481200090939_ref011","doi-asserted-by":"publisher","DOI":"10.2307\/2182169"},{"key":"S0022481200090939_ref015","first-page":"107","article-title":"On the rules of proof in the pure functional calculus","volume":"16","author":"Mostowski","year":"1951","journal-title":"this Journal"},{"key":"S0022481200090939_ref006","first-page":"5","article-title":"On the rules of supposition informal logic","volume":"1","author":"Jaskowski","year":"1934","journal-title":"Studia logica"},{"key":"S0022481200090939_ref002","first-page":"688","article-title":"A logic of actual and possible objects","volume":"31","author":"Cochiarella","year":"1966","journal-title":"this Journal"},{"key":"S0022481200090939_ref003","first-page":"197","article-title":"Quantification and the empty domain","volume":"18","author":"Hailperin","year":"1953","journal-title":"this Journal"},{"key":"S0022481200090939_ref005","volume-title":"The elements of formal logic","author":"Hughes","year":"1965"},{"key":"S0022481200090939_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01969434"},{"key":"S0022481200090939_ref008","volume-title":"Introduction to metamathematics","author":"Kleene","year":"1952"},{"key":"S0022481200090939_ref009","first-page":"83","article-title":"Semantical considerations on modal logic","author":"Kripke","year":"1963","journal-title":"Acta philosophica fennica"},{"key":"S0022481200090939_ref010","first-page":"328","article-title":"A translation theorem for two systems of free logic","author":"Lambert","year":"1967","journal-title":"Logique et analyse"},{"key":"S0022481200090939_ref018","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093958620"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200090939","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T19:12:02Z","timestamp":1559416322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200090939\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1970,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1970,6]]}},"alternative-id":["S0022481200090939"],"URL":"https:\/\/doi.org\/10.2307\/2270518","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1970,6]]}}}