Toward a Layered Ontology of Semantic Duality: 14 Candidate Dualities Across 6 Algebraic Layers with Preliminary Domain and Neural Evidence

We present a formal ontological framework in which conceptual complexity emerges from 14+ candidate dualities organized across 6 algebraic layers (Boolean, Fuzzy, Ordinal, Modal, Trivalent, Probabilistic). The framework is grounded in 72 semantic primitives connected by a directed acyclic graph (DAG) of 133+ dependency edges. We evaluate the framework through three independent methodologies: (1) domain analysis across 8 disciplines and 3 negative controls (Astrology, Alchemy, Phrenology) using a composite 6-metric Domain Validity Score (DVS), achieving DVS ≥ 0.719 for all 8 positive domains while all 3 negative controls fall below the 0.50 threshold (gap = 0.233, robust across all weight configurations); (2) Bayesian model comparison yielding a Bayes factor of 121.4 (decisive) over the reversed ordering, though only anecdotal evidence over alternative philosophical orderings (BF = 1.14 vs. Hegel, 1.95 vs. Peirce); and (3) neurosymbolic learning via a GPT-2 Medium model augmented with a 72-bit triadic head, which learns the primitive structure at 90.8% bit accuracy (though this barely exceeds the 90.3% majority-class baseline due to target sparsity) while preserving general language ability (PPL = 31.95, identical to baseline). The learned representations exhibit near-perfect relational structure (Regla de Tres cosine = 0.996) and show a significant phase transition during training (p = 0.0004). We report both confirmatory and null results transparently: layer ordering in neural representations is not significant (p = 0.71), and only 5 of 13 dual axes show significant learned anti-correlation after FDR correction.