{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T05:57:46Z","timestamp":1789883866151,"version":"4.0.1"},"reference-count":16,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Database Syst."],"published-print":{"date-parts":[[2007,11]]},"abstract":"<jats:p>\n                    A schema mapping is a specification that describes how data structured under one schema (the source schema) is to be transformed into data structured under a different schema (the target schema). Although the notion of an inverse of a schema mapping is important, the exact definition of an inverse mapping is somewhat elusive. This is because a schema mapping may associate many target instances with each source instance, and many source instances with each target instance. Based on the notion that the composition of a mapping and its inverse is the identity, we give a formal definition for what it means for a schema mapping M\u2032 to be an inverse of a schema mapping M for a class S of source instances. We call such an inverse an S-\n                    <jats:italic>inverse<\/jats:italic>\n                    . A particular case of interest arises when S is the class of all source instances, in which case an S-inverse is a global inverse. We focus on the important and practical case of schema mappings specified by source-to-target tuple-generating dependencies, and uncover a rich theory. When S is specified by a set of dependencies with a finite chase, we show how to construct an S-inverse when one exists. In particular, we show how to construct a global inverse when one exists. Given M and M\u2032, we show how to define the largest class S such that M\u2032 is an S-inverse of M.\n                  <\/jats:p>","DOI":"10.1145\/1292609.1292615","type":"journal-article","created":{"date-parts":[[2007,11,30]],"date-time":"2007-11-30T09:24:58Z","timestamp":1196414698000},"page":"25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":80,"title":["Inverting schema mappings"],"prefix":"10.1145","volume":"32","author":[{"given":"Ronald","family":"Fagin","sequence":"first","affiliation":[{"name":"IBM Almaden Research Center, San Jose, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2007,11]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Arenas M. 2006. 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A.","year":"2003"},{"key":"e_1_2_1_4_1","volume-title":"SIAM-AMS Proceedings","volume":"7","author":"Fagin R.","year":"1974"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/320557.320571"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1142351.1142359"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/1085304.1085309"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1061318.1061323"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1114244.1114249"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1265530.1265548"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/0215061"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/543613.543644"},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","volume-title":"Generic Model Management: Concepts and Algorithms","author":"Melnik S.","DOI":"10.1007\/b97859"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1066157.1066177"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/320544.320549"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the International Conference on Very Large Data Bases (VLDB). 1006--1017","author":"Yu C."}],"container-title":["ACM Transactions on Database Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1292609.1292615","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1292609.1292615","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:52:27Z","timestamp":1750243947000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1292609.1292615"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["10.1145\/1292609.1292615"],"URL":"https:\/\/doi.org\/10.1145\/1292609.1292615","relation":{},"ISSN":["0362-5915","1557-4644"],"issn-type":[{"value":"0362-5915","type":"print"},{"value":"1557-4644","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]},"assertion":[{"value":"2007-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}