{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T05:41:56Z","timestamp":1747546916486},"reference-count":10,"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":8046,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that the set of all recursive functions cannot be inferred using first-order queries in the query language containing extra symbols [+ , &lt;]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+, &lt;]. Additionally, we resolve an open question in [7] about passive versus active learning.<\/jats:p>","DOI":"10.2307\/2275176","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:43:45Z","timestamp":1146955425000},"page":"53-81","source":"Crossref","is-referenced-by-count":13,"title":["Learning via queries in [+, &lt;]"],"prefix":"10.1017","volume":"57","author":[{"given":"William I.","family":"Gasarch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark G.","family":"Pleszkoch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Solovay","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200023173_ref007","first-page":"130","volume-title":"Journal of the Association of Computing Machinery","author":"Gasarch","year":"1988"},{"key":"S0022481200023173_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(88)90046-6"},{"key":"S0022481200023173_ref006","first-page":"327","volume-title":"Machine Learning","author":"Gasarch","year":"1990"},{"key":"S0022481200023173_ref010","doi-asserted-by":"publisher","DOI":"10.1145\/322344.322356"},{"key":"S0022481200023173_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(83)90061-0"},{"key":"S0022481200023173_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(88)90019-3"},{"key":"S0022481200023173_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(86)80042-0"},{"key":"S0022481200023173_ref003","volume-title":"A mathematical introduction to logic","author":"Enderton","year":"1972"},{"key":"S0022481200023173_ref004","doi-asserted-by":"publisher","DOI":"10.1070\/RM1965v020n04ABEH001188"},{"key":"S0022481200023173_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(67)91165-5"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200023173","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T22:32:40Z","timestamp":1558045960000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200023173\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["S0022481200023173"],"URL":"https:\/\/doi.org\/10.2307\/2275176","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}