Bayesian Semantic Choice Under Misspecification: A Performance-Theoretic Framework

To model semantic choice in Bayesian updating under misspecification, we hold fixed a common update protocol—constraint refinement with envelope readout—together with a common selector and external proper scoring rule, and vary only semantic package geometry. Focusing on misspecification risk and semantic risk (with risk-functional choice treated as contextual), we prove minimal regime-dependent crossover theorems: classical semantics performs better when evidence constraints are truth-aligned, while non-classical packages can outperform in high-unreliability regimes with explicit thresholds in the proved minimal models. We operationalize unreliability by widening admissible evidence bands (with directional bias), as one convenient proxy for model risk. The mechanisms are distinct: overlap slack in LP, deferral slack in intuitionistic semantics, and a propagation-gating quantity derived from relevant-logic implication structure. We also provide structural robustness arguments and an adaptive design sketch, while keeping full richer-family generalization as future work. The contribution is methodological: a disciplined interface for performance-based comparison of semantic commitments under model risk.