We introduce Non-Coherent Modality Theory (NCMT), a higher-categorical framework in which modal structure is equipped with non-coherent transformation data. Unlike classical approaches in modal logic, topos theory, and homotopy type theory, NCMT does not assume coherence or idempotency conditions on modal operations. Instead, modality is represented via oplax 2-cells that encode non-coherent relationships between identity and modality. We construct a minimal formal framework for NCMT using bicategories, introduce a presheaf-based model with non-natural distortion data, and analyze structural consequences of removing coherence assumptions. We show that NCMT structures are not faithfully representable in standard idempotent or monadic modal frameworks, as coherence data is inherently lost under such interpretations. This work is intended as a foundational exploration of non-coherent higher-categorical structures rather than a completed theory of logic.
Yugo Hidaka (Sun,) studied this question.