{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T11:05:43Z","timestamp":1762081543809,"version":"build-2065373602"},"reference-count":10,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T00:00:00Z","timestamp":1671580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FQXi","award":["41001076"],"award-info":[{"award-number":["41001076"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of contextuality, and its demonstration is trivial for inconsistently connected systems (i.e., systems with disturbance). However, it also holds for consistently connected (and even strongly consistently connected) systems, provided one acknowledges that if a given property was not measured in a given context, this information can be used in defining functions among the random variables. Moreover, every inconsistently connected system can be presented as a (strongly) consistently connected system with essentially the same contextuality characteristics.<\/jats:p>","DOI":"10.3390\/e25010006","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T06:11:24Z","timestamp":1671603084000},"page":"6","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Contextuality and Informational Redundancy"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1909-7706","authenticated-orcid":false,"given":"Ehtibar N.","family":"Dzhafarov","sequence":"first","affiliation":[{"name":"Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janne V.","family":"Kujala","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Turku, FI-20014 Turun yliopisto, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20160389","DOI":"10.1098\/rsta.2016.0389","article-title":"Contextuality in canonical systems of random variables","volume":"375","author":"Dzhafarov","year":"2017","journal-title":"Philos. Trans. R. Soc. A"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"042119","DOI":"10.1103\/PhysRevA.101.042119","article-title":"Contextuality and noncontextuality measures and generalized Bell inequalities for cyclic systems","volume":"101","author":"Dzhafarov","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_3","unstructured":"Tezzin, A., Jones, M., Wolfe, E., and Amaral, B. (2022, November 21). Theorem for Extending Contextuality to Disturbing Systems. Abstract for QCQMB Workshop. Available online: http:\/\/www.psych.purdue.edu\/~ehtibar\/QCQMB2022\/files\/0AbstractsQCQMB2022.pdf."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dzhafarov, E.N. (2017). Replacing nothing with something special: Contextuality-by-Default and dummy measurements. Quantum Foundations, Probability and Information, Springer.","DOI":"10.1007\/978-3-319-74971-6_5"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"052115","DOI":"10.1103\/PhysRevA.87.052115","article-title":"Condition for macroscopic realism beyond the Leggett-Garg inequalities","volume":"87","author":"Kofler","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_6","first-page":"1","article-title":"Leggett-Garg inequalities, pilot waves and contextuality","volume":"1","author":"Bacciagaluppi","year":"2017","journal-title":"Int. J. Quant. Found."},{"key":"ref_7","unstructured":"Palmigiano, A., and Sadrzadeh, M. (2022). The Contextuality-by-Default view of the Sheaf-Theoretic approach to contextuality. Samson Abramsky on Logic and Structure in Computer Science and Beyond, Springer Nature."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"113036","DOI":"10.1088\/1367-2630\/13\/11\/113036","article-title":"The sheaf-theoretic structure of non-locality and contextuality","volume":"13","author":"Abramsky","year":"2011","journal-title":"New J. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"072202","DOI":"10.1063\/1.5024885","article-title":"Necessary conditions for extended noncontextuality in general sets of random variables","volume":"59","author":"Amaral","year":"2018","journal-title":"J. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"050504","DOI":"10.1103\/PhysRevLett.119.050504","article-title":"The contextual fraction as a measure of contextuality","volume":"119","author":"Abramsky","year":"2017","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/6\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:45:20Z","timestamp":1760147120000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/1\/6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,21]]},"references-count":10,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["e25010006"],"URL":"https:\/\/doi.org\/10.3390\/e25010006","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,12,21]]}}}