Year: 2026
Type: article
Abstract: Standard quantum logics are typically defined over the orthomodular lattice associated with Hilbert space, yet there is no consensus on how this structure should be interpreted logically or ontologically. This paper offers a unified perspective on these issues by combining an epistemological three-layer model for scientific theories with quantum set theory. We argue that quasi-set theory is best understood not as an alternative semantics for quantum logics, but as an ontological framework operating at a different epistemological level: the ontological one. From this standpoint, the distinctive non-classical features of quantum logic are explained by representational assumptions about identity and individuality, rather than by positing any direct revisions of the logical principles themselves.
Authors: J. A. F. Cuesta, J. P. Jorge
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7141004737