{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:30Z","timestamp":1760240490382,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T00:00:00Z","timestamp":1561593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called \u201cquantum computation with mixed states\u201d, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of \u201cholistic\u201d contradiction.<\/jats:p>","DOI":"10.3390\/e21070636","type":"journal-article","created":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T11:26:18Z","timestamp":1561634778000},"page":"636","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Holistic Type Extension for Classical Logic via Toffoli Quantum Gate"],"prefix":"10.3390","volume":"21","author":[{"given":"Hector","family":"Freytes","sequence":"first","affiliation":[{"name":"Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roberto","family":"Giuntini","sequence":"additional","affiliation":[{"name":"Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy"},{"name":"Centro Linceo Interdisciplinare \u201cB. Segre\u201d, 00165 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3650-5858","authenticated-orcid":false,"given":"Giuseppe","family":"Sergioli","sequence":"additional","affiliation":[{"name":"Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3293","DOI":"10.1007\/s10773-013-1696-y","article-title":"A quantum computational semantics for epistemic logical operators. Part II: Semantics","volume":"53","author":"Beltrametti","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chiara, M.L.D., Giuntini, R., Leporini, R., and Sergioli, G. (2018). 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