Internalizing Universal Law: A Paraconsistent Reconstruction of Kant's Categorical Imperative

PDK is a paraconsistent, dynamic reconstruction of Kant’s Categorical Imperative (CI). Its central move is to internalize universalizability not as a meta-level test but as a model update: an "everyone adopts M" operator that transforms the practice structure and then re-evaluates norms. Built on a four-valued (Belnap-Dunn) base with an LFI-style consistency test and neighborhood semantics for obligation, PDK tolerates genuine moral tensions without explosion while preserving disciplined deontic reasoning through consistency and feasibility guards. Two CI tests are formalized in the object language---no contradiction in conception and no contradiction in the will---and both are evaluated after update. A CI rule licenses duty only when both tests pass; autonomy appears as fixed-point stability of those tests under their own universalization. Technically, reduction schemata eliminate update operators into a static core; the paper proves soundness, establishes relative completeness for the propositional dynamic fragment, derives a finite model property and PSPACE-completeness for that fragment, and marks undecidability frontiers for first-order extensions. An impossibility landscape explains why the guarded design is necessary: unguarded classical deontics plus a strong CI trivialize; no static surrogate exists for update; harmless commuting updates are vacuous; strong “ought implies can” fails under reflective resource limits; and update nesting yields a strict depth hierarchy. Case studies (lying promise, promise vs. rescue, self-defeating maxims, harmless beneficence, order sensitivity) illustrate the logic’s behavior. Philosophically, PDK isolates a logical core of transcendental normativity: update invariance and fixed-point stability, and, in this reconstruction, offers a novel structural reading of Kantian transcendentality as self-invariance under universalization.