Consistency Is Not Correctness: What Internal Contradiction Detection Certifies, Why the Entailment Is Disjunctive, and Which Decisions It Leaves Unlicensed

@misc{mahendrakar2026consistency,
  author       = {Mahendrakar, Pranay},
  title        = {{Consistency Is Not Correctness: What Internal Contradiction Detection Certifies, Why the Entailment Is Disjunctive, and Which Decisions It Leaves Unlicensed}},
  year         = {2026},
  month        = sep,
  date         = {2026-09-07},
  publisher    = {Life of Research},
  doi          = {10.5281/zenodo.22559866},
  url          = {https://lifeofresearch.com/articles/9},
  abstract     = {(c) 2026 Pranay Mahendrakar. Licensed under CC BY 4.0. Contradiction detection occupies an unusual position among proposals for making a language model check itself. Comparing two of a model's own outputs appears to need no external oracle, which makes it look like the one exception to the observation that working hallucination detectors sit outside the model. This paper argues that the appearance is produced by running two different inferences under one word. Inconsistency supports a deductive inference: if two outputs contradict each other, at least one of them is false, and this follows from logic alone without any appeal to the world. Consistency supports only an inductive one: agreement is evidence of correctness to the extent that the model's errors are unstable under whatever perturbation produced the second output, an assumption that the sampling-based detectors state explicitly and that the strongest published instance of the family declines to extend to systematic error. The two inferences have opposite properties. The deductive one is sound and disjunctive, identifying that something is wrong without identifying which output is wrong, and so licenses withholding but not repair. The inductive one names a specific output to accept, and fails in the cases that matter most, because an error shared by both compared outputs survives the comparison intact. The paper traces the consequences: that breaking the disjunction requires an adjudicator whose errors are not those of the generator, that every published route to one is external in the relevant sense even when it runs on the same weights, and that a consistency rate is a measurement of distributional stability under a named perturbation rather than a reliability figure. Making consistency an optimization target inverts its diagnostic value, which two recent results on label-free training report directly. What is not known is stated flatly, and six measurements are specified. The literature search, drafting and citation verification for this paper were carried out with AI assistance under the author's direction. Every citation was machine-verified against the arXiv API and Crossref before inclusion, and every quantitative claim was read back against the cited source's own abstract or, where a claim is drawn from a paper's body, against the located passage. The author is responsible for the final text and for all claims made in it.},
  keywords     = {self-consistency, hallucination detection, internal contradiction, generator-validator gap, abstention, self-correction, verification, calibration},
  language     = {en},
  copyright    = {Creative Commons Attribution 4.0}
}