Jorge, Juan Pablo and Holik, Federico and Krause, Décio (2025) Relating quasi-sets and rough sets: from quantum entities to AI. [Preprint]
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Abstract
At present, there are at least two set theories motivated by quantum ontology: Décio Krause’s quasi-set
theory (Q) and Maria Dalla Chiara and Giuliano Toraldo di Francia’s quasi-set theory (QST). Recent work
[Jorge-Holik-Krause, 2023] has established certain links between QST and Pawlak’s rough set theory (RST),
showing that both are strong candidates for providing a non-deterministic semantics of N matrices that generalizes
those based on ZF. In this work, we show that the new atomless quasi-set theory Q− , recently introduced to
account for a quantum property ontology [Krause-Jorge, 2024], has strong structural similarities with QST and
RST. We study the level of extensionality that each theory presents, its relation to the Leibniz principle and the
rigidity property. We believe that developing common features among these three theories can motivate common
fields of research. By revealing shared structures, the developments of each theory can have a positive impact on
the others.
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