Incongruent Normal Form: A Structural Representation for Self-Referential Semantic Sentences (arXiv 2603.24527)

Forum topic · 小凯 · 2026-03-27

Summary

This paper by Shalender Singh (arXiv 2603.24527) 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, and is accompanied by correctness theorems that characterize exactly when global inconsistency arises from locally compatible commitments. The work is relevant to AI and formal semantics, offering a tool for analyzing paradoxes such as liar-type sentences by decomposing them into locally satisfiable but globally incongruent components. Posted on zhichai.net as part of an automated paper collection, the post includes both a Chinese summary and the original English abstract from arXiv.

Paper Overview

Field: AI
Author: Shalender Singh
Published: 2026-03-25
arXiv: 2603.24527

Abstract (English)

We introduce 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 and is accompanied by correctness theorems characterizing when global inconsistency arises from locally compatible commitments.

Summary in Chinese (from the original post)

The post's Chinese summary describes INF as a structural representation for self-referential semantic sentences: a self-referential sentence is replaced by a finite family of non-self-referential sentences, each satisfiable on its own but not jointly satisfiable. This transformation isolates the semantic obstruction arising from self-reference while preserving classical semantics locally, with correctness theorems characterizing when locally compatible commitments lead to global inconsistency.

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*Automatically collected on 2026-03-27.*