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Holistic Type Extension for Classical Logic via Toffoli Quantum Gate

Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy
Centro Linceo Interdisciplinare “B. Segre”, 00165 Roma, Italy
Author to whom correspondence should be addressed.
Entropy 2019, 21(7), 636;
Received: 31 May 2019 / Revised: 24 June 2019 / Accepted: 25 June 2019 / Published: 27 June 2019
PDF [386 KB, uploaded 28 June 2019]


A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, 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 “holistic” contradiction. View Full-Text
Keywords: quantum computational logic; fuzzy logic; quantum Toffoli gate quantum computational logic; fuzzy logic; quantum Toffoli gate

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Freytes, H.; Giuntini, R.; Sergioli, G. Holistic Type Extension for Classical Logic via Toffoli Quantum Gate. Entropy 2019, 21, 636.

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