Incongruent Normal Form: Self-Reference as Locally Satisfiable but Globally Inconsistent

Summary

This arXiv paper (2603.24527) by Shalender Singh, posted on zhichai.net, introduces incongruent normal form (INF), a structural representation for self-referential semantic sentences. An INF replaces a self-referential sentence with a finite family of non-self-referential sentences that are individually satisfiable but not jointly satisfiable. This transformation isolates the semantic obstruction created by self-reference while preserving classical semantics locally. The work is accompanied by correctness theorems that characterize exactly when global inconsistency arises from locally compatible commitments. The approach offers a new lens on classic self-reference paradoxes, such as the liar family, by decomposing them into finitely many ordinary sentences whose local satisfiability cannot be combined into a single model. Relevant to AI, logic, and formal semantics research.