{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:10:05Z","timestamp":1775167805694,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T00:00:00Z","timestamp":1621036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Automated reasoning is becoming crucial for information systems. Building one uniform decision support system has become too complicated. The natural approach is to divide the task and combine the results from different subsystems into one uniform answer. It is the basic idea behind the system approach, where one solution is a composition of multiple subsystems. In this paper, the main emphasis is on establishing the theoretical framework that combines various reasoning methods into a collective system. The system\u2019s formal abstraction uses graph theory and provides a discussion on possible aggregation function definitions. The proposed framework is a tool for building and testing specific approaches rather than the solution itself.<\/jats:p>","DOI":"10.3390\/axioms10020091","type":"journal-article","created":{"date-parts":[[2021,5,16]],"date-time":"2021-05-16T23:17:16Z","timestamp":1621207036000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["The Formal Framework for Collective Systems"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4632-7709","authenticated-orcid":false,"given":"Rafa\u0142","family":"Palak","sequence":"first","affiliation":[{"name":"Department of Applied Informatics, Faculty of Management and Computer Science, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"},{"name":"Facultad de Inform\u00e1tica, Complutense University of Madrid, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7851-4330","authenticated-orcid":false,"given":"Krystian","family":"Wojtkiewicz","sequence":"additional","affiliation":[{"name":"Department of Applied Informatics, Faculty of Management and Computer Science, Wroc\u0142aw University of Science and Technology, 50-370 Wroc\u0142aw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.ins.2009.08.001","article-title":"From social computing to reflexive collective intelligence: The IEML research program","volume":"180","year":"2010","journal-title":"Inf. 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