{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:35:57Z","timestamp":1758274557259,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We investigate a number of semantically defined fragments of Tarski's algebra\nof binary relations, including the function-preserving fragment. We address the\nquestion whether they are generated by a finite set of operations. We obtain\nseveral positive and negative results along these lines. Specifically, the\nhomomorphism-safe fragment is finitely generated (both over finite and over\narbitrary structures). The function-preserving fragment is not finitely\ngenerated (and, in fact, not expressible by any finite set of guarded\nsecond-order definable function-preserving operations). Similarly, the\ntotal-function-preserving fragment is not finitely generated (and, in fact, not\nexpressible by any finite set of guarded second-order definable\ntotal-function-preserving operations). In contrast, the forward-looking\nfunction-preserving fragment is finitely generated by composition,\nintersection, antidomain, and preferential union. Similarly, the\nforward-and-backward-looking injective-function-preserving fragment is finitely\ngenerated by composition, intersection, antidomain, inverse, and an `injective\nunion' operation.<\/jats:p>","DOI":"10.46298\/lmcs-20(3:20)2024","type":"journal-article","created":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T08:25:55Z","timestamp":1725438355000},"source":"Crossref","is-referenced-by-count":1,"title":["Preservation theorems for Tarski's relation algebra"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"given":"Bart","family":"Bogaerts","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Balder ten","family":"Cate","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brett","family":"McLean","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan Van den","family":"Bussche","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2024,9,4]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14201\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14201\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T08:25:55Z","timestamp":1725438355000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11328"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:20)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2305.04656v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2305.04656v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2305.04656v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2305.04656","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2305.04656","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,9,4]]},"article-number":"11328"}}