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

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.