System Logic Theory: A Theory for Judging Whether Logical Structures Are Valid

This paper constructs a meta-theoretical framework—System Logic Theory (K-Theory)—centered on "systems" and "models," aiming to provide a unified logical grammar for the determination of propositional values, the diagnosis of paradoxes, and the analysis of thought experiments. The paper reveals the incompleteness of the four traditional laws of logic and proposes a three‑world system model (Hardware Law, Wireless Law, Software Law) that distinguishes the information systems involved in human cognition into the first world (objective matter), the second world (individual cognition), and the third world (social consensus). As the foundation of System Logic Theory, four axioms are established—the System Definition Axiom, System Consistency Axiom, System Dynamics Axiom, and Propositional Value Consistency Axiom—from which fourteen theorems are derived, forming a complete logical judgment system. System Logic Theory passes all the tests of its own axioms, demonstrating that it is non‑self‑referential, non‑self‑contradictory, deduction‑closed, and truth‑grounded. At the application level, this paper uses System Logic Theory to falsify the self‑referential paradox, the barber paradox, and the set‑theoretic paradox, diagnoses the illegitimate construction of classic thought experiments such as the Veil of Ignorance and the free‑will‑versus‑determinism debate, and proposes a "system transition" theory that provides a unified logical grammar for conceptual evolution in the history of mathematics and science. System Logic Theory also incorporates the important results of Gödel’s incompleteness theorems. Meanwhile, this paper declares the boundaries of System Logic Theory: its legitimacy judgments are normatively effective only for K‑models that accept its four axioms and pass K‑verification.