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Logic"],"published-print":{"date-parts":[[2023,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An algebraic proof is presented for the finite strong standard completeness of the Involutive Uninorm Logic with Fixed Point (<jats:inline-formula><jats:alternatives><jats:tex-math>$${{\\mathbf {IUL}}^{fp}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mrow>\n                      <mml:mi>IUL<\/mml:mi>\n                    <\/mml:mrow>\n                    <mml:mrow>\n                      <mml:mi>fp<\/mml:mi>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>). It may provide a first step towards settling the standard completeness problem for the Involutive Uninorm Logic (<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbf {IUL}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>IUL<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, posed in G. Metcalfe, F. Montagna. (J Symb Log 72:834\u2013864, 2007)) in an algebraic manner. The result is proved via an embedding theorem which is based on the structural description of the class of odd involutive FL<jats:inline-formula><jats:alternatives><jats:tex-math>$$_e$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mrow\/>\n                    <mml:mi>e<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-chains which have finitely many positive idempotent elements.\n<\/jats:p>","DOI":"10.1007\/s00153-022-00839-1","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T20:02:38Z","timestamp":1658520158000},"page":"67-86","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Involutive Uninorm Logic with Fixed Point enjoys finite strong standard completeness"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8664-4226","authenticated-orcid":false,"given":"S\u00e1ndor","family":"Jenei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"unstructured":"B\u011bhounek, L., Cintula, P., H\u00e1jek, P.: Introduction to Mathematical Fuzzy Logic. 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