{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T12:27:53Z","timestamp":1765974473125,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T00:00:00Z","timestamp":1664841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Health Sciences of the University of Florence"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognition; in doing so, we will show how the interplay between formal language and metalanguage allows for characterizing pure quantum states as infinite singletons: in the case of the spin observable, we obtain an equation defining a modality that is then re-interpreted as an abstract projection operator. By including a temporal parameter in the equations and by defining a modal negative operator, we derive an intuitionistic-like negation, for which the non-contradiction law is seen as an equivalent of the quantum uncertainty. Building on the psychoanalytic theory of Bi-Logic by Matte Blanco, we use modalities in interpreting the emergence of conscious representations from an unconscious one, and we demonstrate that this description fits well with Freud\u2019s view of the role of negation in mental processes. Psychoanalysis, where affect plays a prominent role in shaping not only conscious, but also unconscious representations, is therefore seen as a suitable model to expand the domain of quantum cognition to the broader field of affective quantum cognition.<\/jats:p>","DOI":"10.3390\/e24101419","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T04:04:56Z","timestamp":1665201896000},"page":"1419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Modal Interpretation of Quantum Spins and Its Application to Freudian Theory"],"prefix":"10.3390","volume":"24","author":[{"given":"Giulia","family":"Battilotti","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Padua, Via Trieste, 63, 35122 Padova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milo\u0161","family":"Borozan","sequence":"additional","affiliation":[{"name":"Department of Neurosciences, Imaging and Clinical Sciences, G. d\u2019Annunzio University of Chieti-Pescara, Via dei Vestini, 31, 66100 Chieti, Italy"},{"name":"Center for Advanced Studies and Technologies (C.A.S.T.), Via Luigi Polacchi, 11, 66100 Chieti, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9573-0043","authenticated-orcid":false,"given":"Rosapia Lauro","family":"Grotto","sequence":"additional","affiliation":[{"name":"Department of Health Sciences, University of Florence, Via San Salvi, 12, 50135 Firenze, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,4]]},"reference":[{"key":"ref_1","unstructured":"Conrotto, F. (2005). Tra il Sapere e la Cura. Un itinerario Freudiano, Franco Angeli."},{"key":"ref_2","unstructured":"Enriques, F. (1906). Problemi Della Scienza, Zanichelli."},{"key":"ref_3","unstructured":"Feferman, S., Kleene, S., Moore, G., Solovay, R., and Van Heijenoort, J. (1986). On formally undecidable propositions of Principia Mathematica and related systems. Kurt G\u00f6del, Collected Works: Volume I: Publications 1929\u20131936, Oxford University Press."},{"key":"ref_4","unstructured":"Lauro Grotto, R. (2014). Paradigmi Metapsicologici, ETS."},{"key":"ref_5","unstructured":"Stengel, E. (2002). Zur Auffassung der Aphasien. Eine Kritische Studie [On Aphasia: A Critical Study] (1891), International Universities."},{"key":"ref_6","unstructured":"Freud, S. (1900). The Interpretation of Dreams. Standard Edition, Hogarth Press."},{"key":"ref_7","unstructured":"Matte Blanco, I. (1975). The Unconscious as Infinite Sets, Duckworth."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3488","DOI":"10.1007\/s10773-013-1823-9","article-title":"Quantum states as virtual singletons: Converting duality into symmetry","volume":"53","author":"Battilotti","year":"2014","journal-title":"Int. J. Theor. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"979","DOI":"10.2307\/2586685","article-title":"Basic logic: Reflection, symmetry, visibility","volume":"65","author":"Sambin","year":"2000","journal-title":"J. Symb. Log."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1023\/A:1026652903971","article-title":"From basic logic to quantum logics with cut-elimination","volume":"37","author":"Faggian","year":"1998","journal-title":"Int. J. Theor. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Crosilla, L., and Schuster, P. (2005). Toward a minimalist foundation for constructive mathematics. From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780198566519.001.0001"},{"key":"ref_12","unstructured":"Feferman, S., Kleene, S., Moore, G., Solovay, R., and Van Heijenoort, J. (1986). An interpretation of the intuitionistic propositional calculus. Kurt G\u00f6del, Collected Works: Volume I: Publications 1929\u20131936, Oxford University Press."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Masini, A., and Zorzi, M. (2019). A Logic for Quantum Register Measurements. Axioms, 8.","DOI":"10.3390\/axioms8010025"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1006\/jtbi.1997.0604","article-title":"Human subconscious as a p-adic dynamical system","volume":"193","author":"Khrennikov","year":"1998","journal-title":"J. Theor. Biol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0303-2647(00)00077-0","article-title":"Classical and quantum dynamics on p-adic trees of ideas","volume":"56","author":"Khrennikov","year":"2000","journal-title":"Biosystems"},{"key":"ref_16","unstructured":"Khrennikov, A. (2002). Classical and Quantum Mental Models and Freud\u2019s Theory of Unconscious\/Conscious Mind, V\u00e4xj\u00f6 University Press."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"46","DOI":"10.7565\/landp.v10i2.5795","article-title":"Infinite singletons and the logic of Freudian theory","volume":"10","author":"Battilotti","year":"2021","journal-title":"Lang. Psychoanal."},{"key":"ref_18","first-page":"235","article-title":"Negation","volume":"Volume 19","author":"Freud","year":"1925","journal-title":"Standard Edition"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1111\/j.1747-9991.2011.00418.x","article-title":"Proof theory for modal logic","volume":"6","author":"Negri","year":"2011","journal-title":"Philos. Compass"},{"key":"ref_20","first-page":"245","article-title":"Notwithstanding Bohr, the reasons for QBism","volume":"15","author":"Fuchs","year":"2017","journal-title":"Mind Matter"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1142\/S021974990500089X","article-title":"Qubits and Quantum Spaces","volume":"3","author":"Zizzi","year":"2005","journal-title":"Int. J. Quantum Inf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1142\/S0219749905000591","article-title":"Basic logic and quantum computing: Logical judgements by an insider observer","volume":"2005","author":"Battilotti","year":"2005","journal-title":"Int. J. Quantum Inf."},{"key":"ref_23","unstructured":"Battilotti, G., and Zizzi, P. (2004). Logical interpretation of a reversible measurement in quantum computing. arXiv."},{"key":"ref_24","unstructured":"Feferman, S., Kleene, S., Moore, G., Solovay, R., and Van Heijenoort, J. (1986). On the intuitionistic propositional calculus. Kurt G\u00f6del, Collected Works: Volume I: Publications 1929\u20131936, Oxford University Press."},{"key":"ref_25","first-page":"183","article-title":"Sur quelques points de la Logique de M. Brouwer","volume":"5","author":"Glivenko","year":"1929","journal-title":"Bull. Acad. Des Sci. Belg."},{"key":"ref_26","first-page":"159","article-title":"The Unconscious","volume":"Volume 14","author":"Freud","year":"1915","journal-title":"Standard Edition"},{"key":"ref_27","unstructured":"Geach, P.T., and Black, M. (1952). Function and Concept. Translations From the Philosophical Writings of Gottlob Frege, Blackwell."},{"key":"ref_28","unstructured":"Geach, P.T., and Black, M. (1952). On Concept and Object. Translations From the Philosophical Writings of Gottlob Frege, Blackwell."},{"key":"ref_29","unstructured":"Borozan, M. (2017). When the Possible Becomes Necessary: Towards a Formalization of Matte Blanco\u2019s Bi-Logic. [Master\u2019s Thesis, University of Florence]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1093\/brain\/awq010","article-title":"The default-mode, ego-functions and free-energy: A neurobiological account of Freudian ideas","volume":"133","author":"Friston","year":"2010","journal-title":"Brain"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.neuropsychologia.2013.10.003","article-title":"Linking psychoanalysis with neuroscience: The concept of ego","volume":"55","author":"Rizzolatti","year":"2014","journal-title":"Neuropsychologia"},{"key":"ref_32","first-page":"123","article-title":"Freud\u2019s \u201cProject for a Scientific Psychology\u201d after 100 Years: The Unconscious Mind in the Era of Cognitive Neuroscience","volume":"2","author":"Woody","year":"1995","journal-title":"Philos. Psychiatry Psychol."},{"key":"ref_33","unstructured":"Ricoeur, P. (1970). Freud and Philosophy: An Essay on Interpretation, Yale University Press."},{"key":"ref_34","first-page":"629","article-title":"On Dreams","volume":"Volume 5","author":"Freud","year":"1901","journal-title":"Standard Edition"},{"key":"ref_35","unstructured":"Langer, S. (1953). Feeling and Form, Charles Scribners\u2019 Sons."},{"key":"ref_36","first-page":"139","article-title":"An Outline of Psycho-Analysis","volume":"Volume 23","author":"Freud","year":"1938","journal-title":"Standard Edition"},{"key":"ref_37","unstructured":"Hermann, I. (1989). Das Ich und das Denken: Eine psychoanalytische Studie [The Ego and Thinking: A Psychoanalytic Study], Psicoanalisi e Logica."},{"key":"ref_38","unstructured":"Arieti, S. (1974). Interpretation of Schizophrenia, Basic Books. [2nd ed.]."},{"key":"ref_39","unstructured":"Dedekind, R. (1901). Theory of Numbers, The Open Court Publishing Company."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"83","DOI":"10.4018\/ijcini.2014100105","article-title":"Symmetry vs. duality in logic: An interpretation of Bi-logic to model cognitive processes beyond inference","volume":"8","author":"Battilotti","year":"2014","journal-title":"Int. J. Cogn. Inform. Nat. Intell."},{"key":"ref_41","unstructured":"Aerts, D., Dalla Chiara, M.L., De Ronde, C., and Krause, D. (2018). Probing the Meaning of Quantum Mechanics: Information, Contextuality, Relationalism and Entanglement, World Scientific Publishing."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1038\/s42005-021-00589-1","article-title":"A no-go theorem for the persistent reality of Wigner\u2019s friend perception","volume":"4","author":"Baumann","year":"2021","journal-title":"Commun. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3711","DOI":"10.1038\/s41467-018-05739-8","article-title":"Quantum theory cannot consistently describe the use of itself","volume":"9","author":"Frauchiger","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s10699-017-9524-0","article-title":"Towards Better Understanding QBism","volume":"23","author":"Khrennikov","year":"2018","journal-title":"Found. Sci."},{"key":"ref_45","unstructured":"Jammer, M. (1974). The Philosophy of Quantum Mechanics, Wiley & Sons."},{"key":"ref_46","unstructured":"Colodny, R. (1972). A formal approach to the philosophy of science. Paradigms and Paradoxes: The Philosophical Challenge of the Quantum Domain, University of Pittsburgh Press."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1134\/S2070046616040014","article-title":"Formal foundations for the origins of human consciousness","volume":"8","author":"Iurato","year":"2016","journal-title":"p-adic Numbers Ultrametric Anal. Appl."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1353\/aim.2008.0009","article-title":"The Unconscious as an Ultrametric Set","volume":"64","year":"2007","journal-title":"Am. Imago"},{"key":"ref_49","first-page":"IV","article-title":"Special Issue on Computational Psychoanalysis","volume":"8","author":"Murtagh","year":"2014","journal-title":"Int. J. Cogn. Inform. Nat. Intell."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s12304-022-09487-7","article-title":"Natural code of subjective experience","volume":"15","author":"Surov","year":"2022","journal-title":"Biosemiotics"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1007\/s10699-020-09712-x","article-title":"Quantum cognitive triad: Semantic geometry of context representation","volume":"26","author":"Surov","year":"2021","journal-title":"Found. Sci."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"9","DOI":"10.15406\/jpcpy.2022.13.00706","article-title":"Infinite singletons and the Default Mode Network","volume":"13","author":"Battilotti","year":"2022","journal-title":"J. Psichol. Clin. Psychiatry"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/00207578.2020.1726713","article-title":"On the logic of the unconscious","volume":"101","author":"Saad","year":"2020","journal-title":"Int. J. Psychoanal."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(87)90045-4","article-title":"Linear Logic","volume":"50","author":"Girard","year":"1987","journal-title":"Theor. Comput. Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"888","DOI":"10.2307\/2275915","article-title":"A modal view of linear logic","volume":"59","author":"Martini","year":"1994","journal-title":"J. Symb. Log."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1419\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:46:34Z","timestamp":1760143594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/10\/1419"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,4]]},"references-count":55,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["e24101419"],"URL":"https:\/\/doi.org\/10.3390\/e24101419","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,10,4]]}}}