{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T17:37:59Z","timestamp":1782927479069,"version":"3.54.5"},"reference-count":73,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T00:00:00Z","timestamp":1580169600000},"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>In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.<\/jats:p>","DOI":"10.3390\/e22020156","type":"journal-article","created":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T10:51:07Z","timestamp":1580295067000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Non-Deterministic Semantics for Quantum States"],"prefix":"10.3390","volume":"22","author":[{"given":"Juan Pablo","family":"Jorge","sequence":"first","affiliation":[{"name":"Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federico","family":"Holik","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, 1900 La Plata, Argentina"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,28]]},"reference":[{"key":"ref_1","first-page":"227","article-title":"Non-deterministic Semantics for Logical Systems","volume":"Volume 16","author":"Gabbay","year":"2011","journal-title":"Handbook of Philosophical Logic"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/s11225-009-9196-z","article-title":"What Is a Non-truth-functional Logic?","volume":"92","author":"Marcos","year":"2009","journal-title":"Stud. 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