{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T04:42:22Z","timestamp":1744605742110},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Council for Scientific and Technological Development, Brazil","award":["306530\/2019-8"],"award-info":[{"award-number":["306530\/2019-8"]}]},{"name":"Spanish project","award":["PID2019-111544GB-C21"],"award-info":[{"award-number":["PID2019-111544GB-C21"]}]},{"name":"Spanish Ram\u00f3n y Cajal research program","award":["RYC-2016-19799"],"award-info":[{"award-number":["RYC-2016-19799"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The aim of the paper is to analyze the expressive power of the square operator of \u0141ukasiewicz logic: $\\ast x=x\\odot x$, where $\\odot $ is the strong \u0141ukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the \u0141ukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form $n+1$ where $n$ belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and \u0141ukasiewicz square operator. Finally, we propose an alternative way to account for \u0141ukasiewicz square operator on involutive G\u00f6del chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations.<\/jats:p>","DOI":"10.1093\/logcom\/exab064","type":"journal-article","created":{"date-parts":[[2021,9,16]],"date-time":"2021-09-16T19:16:34Z","timestamp":1631819794000},"page":"767-807","source":"Crossref","is-referenced-by-count":1,"title":["On the expressive power of \u0141ukasiewicz square operator"],"prefix":"10.1093","volume":"32","author":[{"given":"Marcelo E","family":"Coniglio","sequence":"first","affiliation":[{"name":"Centre for Logic , Epistemology and the History of Science - (CLE) and Institute of Philosophy and the Humanities - (IFHC), University of Campinas, 13083-859, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesc","family":"Esteva","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Research Institute (IIIA) , CSIC, Barcelona, 08193, 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