{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T20:17:42Z","timestamp":1649103462111},"reference-count":0,"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":23446,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1950,1]]},"abstract":"<jats:p>The present note suggests how the computation of complexity-values outlined in <jats:italic>The logical simplicity of predicates<\/jats:italic> may be so modified as to satisfy a more stringent requirement than was there imposed.<\/jats:p><jats:p>By the method of computation described in that article, a basis consisting of two two-place predicates has in general the value 6. Any such basis may be replaced by one four-place predicate that is self-complete with respect to two of its places and also with respect to the remaining two. Such a predicate has but one \u201cjoint,\u201d and therefore a value of 5. The consolidation of the two predicates into one thus results in a basis having a lower complexity-value. This does not violate the cardinal rule laid down in that article for testing proposed ways of assigning complexity-values; for, conversely, a four-place predicate that is self-complete in the way described can always be replaced by two two-place prediates. The rule requires a four-place predicate of the kind described to have a higher value than two two-place predicates only if replacement of two two-place predicates by such a four-place predicate is always possible, while replacement of such a four-place predicate by two two-place predicates is not.<\/jats:p><jats:p>However, we might reasonably strengthen our cardinal rule for complexity-valuation by adding as a second requirement:<\/jats:p><jats:p><jats:italic>If each basis of kind A is always replaceable by some basis of kind B, and each basis of kind B is always replaceable by some basis of kind A, then a basis of kind A and a basis of kind B must, in the absence of contrary indications, have the same complexity-value<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2269231","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T19:07:57Z","timestamp":1146942477000},"page":"228-229","source":"Crossref","is-referenced-by-count":2,"title":["An improvement in the theory of simplicity"],"prefix":"10.1017","volume":"14","author":[{"given":"Nelson","family":"Goodman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200105067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T10:23:57Z","timestamp":1559989437000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200105067\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1950,1]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1950,1]]}},"alternative-id":["S0022481200105067"],"URL":"https:\/\/doi.org\/10.2307\/2269231","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1950,1]]}}}