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Title: | Preservation theorems for Tarski's relation algebra | Authors: | Bogaerts, Bart Ten Cate, Balder Mclean, Brett VAN DEN BUSSCHE, Jan |
Issue Date: | 2024 | Publisher: | LOGICAL METHODS COMPUTER SCIENCE E V | Source: | Logical Methods in Computer Science, 20 (3) (Art N° 20) | Abstract: | . We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question of whether they are generated by a finite set of operations. We obtain several positive and negative results along these lines. Specifically, the homomorphism-safe fragment is finitely generated (both over finite and over arbitrary structures). The function-preserving fragment is not finitely generated (and, in fact, not expressible by any finite set of guarded secondorder definable function-preserving operations). Similarly, the total-function-preserving fragment is not finitely generated (and, in fact, not expressible by any finite set of guarded second-order definable total-function-preserving operations). In contrast, the forwardlooking function-preserving fragment is finitely generated by composition, intersection, antidomain, and preferential union. Similarly, the forward-and-backward-looking injectivefunction-preserving fragment is finitely generated by composition, intersection, antidomain, inverse, and an 'injective union' operation. | Notes: | Bogaerts, B (corresponding author), Vrije Univ Brussel, Brussels, Belgium. bart.bogaerts@vub.be; b.d.tencate@uva.nl; brett.mclean@ugent.be; jan.vandenbussche@uhasselt.be |
Document URI: | http://hdl.handle.net/1942/44319 | ISSN: | 1860-5974 | e-ISSN: | 1860-5974 | DOI: | 10.46298/LMCS-20(3:20)2024 | ISI #: | 001307475400001 | Rights: | B. Bogaerts, B. ten Cate, B. McLean, and J. Van den Bussche⃝ CC Creative Commons. This work is licensed under the Creative Commons Attribution License. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, 171 Second St, Suite 300, San Francisco, CA 94105, USA, or Eisenacher Strasse 2, 10777 Berlin, Germany | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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