The Awareness Logic of Ambiguity (ALA): Triadic Interpretive States and Their Structure-Preserving Operational Core

[2608.15093] The Awareness Logic of Ambiguity (ALA): Triadic Interpretive States and Their Structure-Preserving Operational Core Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > General Mathematics arXiv:2608.15093 (math) [Submitted on 15 Aug 2026] Title: The Awareness Logic of Ambiguity (ALA): Triadic Interpretive States and Their Structure-Preserving Operational Core Authors: Seyyed Ahmad Edalatpanah View a PDF of the paper titled The Awareness Logic of Ambiguity (ALA): Triadic Interpretive States and Their Structure-Preserving Operational Core, by Seyyed Ahmad Edalatpanah View PDF HTML (experimental) Abstract: The Awareness Logic of Ambiguity (ALA) is introduced as a formal framework for preserving the structure of judgment before scalar projection. An evaluative act is represented by a triadic interpretive state with three functionally distinct roles: interpretive valuation, contextual alignment, and epistemic restraint. ALA uses a cognitive order with reversed polarity for restraint and shows that the resulting state space forms a bounded distributive lattice. It develops weakly and strictly admissible scalar projections as declared interfaces, together with a role-preserving arithmetic core and canonical permissive and conservative aggregation operators. The Non-Collapse Theorem establishes that two states that are equal after scalar projection may become distinguishable under an ALA lattice operation; hence scalar equality does not imply operational equivalence. The paper also establishes the conditional semantic minimality of the triad and treats the unit cube as the normalized real-valued realization of a more general role architecture. A high-stakes clinical scenario illustrates why evidential support, contextual alignment, and restraint toward action should remain separate until a scalar reporting or decision interface is explicitly chosen. ALA therefore provides a structure-preserving calculus for reasoning under ambiguity before projection. Comments: 41 pages, 6 figures. Published in Journal of Fuzzy Extension and Applications, 7(2) (2026), 661-702 Subjects: General Mathematics (math.GM) MSC classes: 03E72 (Primary), 03G10, 06D05 (Secondary) Cite as: arXiv:2608.15093 [math.GM] (or arXiv:2608.15093v1 [math.GM] for this version) https://doi.org/10.48550/arXiv.2608.15093 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Fuzzy Extension and Applications 7(2) (2026) 661-702 Related DOI : https://doi.org/10.22105/jfea.2026.582827.2294 Focus to learn more DOI(s) linking to related resources Submission history From: Seyyed Ahmad Edalatpanah [ view email ] [v1] Sat, 15 Aug 2026 07:32:33 UTC (71 KB) Full-text links: Access Paper: View a PDF of the paper titled The Awareness Logic of Ambiguity (ALA): Triadic Interpretive States and Their Structure-Preserving Operational Core, by Seyyed Ahmad Edalatpanah View PDF HTML (experimental) TeX Source view license Current browse context: math.GM < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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