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Entailment operator

An entailment operator is a mathematical function that maps a given statement or textual expression to the set of all expressions that logically or semantically entail it. By translating directional implication into a set-containment relationship, the operator identifies the collection of all valid premises, references, or candidate outputs whose truth guarantees the truth of the original statement. In formal semantics, computational logic, and statistical language modeling, this operator is used to construct entailment sets and quantify semantic uncertainty, allowing systems to evaluate correctness, measure informational specificity, and establish statistical guarantees on the factuality of generated language.

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Language Models with Conformal Factuality Guarantees

Language Models with Conformal Factuality Guarantees

Christopher Mohri, Tatsunori Hashimoto

OrganizationsAllen Institute for AIUniversity of California, San Diego

Why you should read this

Proposes a conformal prediction framework that provides rigorous statistical correctness guarantees for black-box language model outputs by progressively pruning uncertain sub-claims while preserving most generated content.

Large language models demonstrate impressive capabilities across diverse tasks yet can generate content unfaithful to external knowledge sources.To enforce controllable generation,this work introduces post-generation techniques for constrained decoding crafted specifically as defensible guards.We introduce SENSE,a framework leveraging span-level evidence to align outputs with desired alignment criteria.Rather than enforcing token-level constraints directly over entire vocabularies,SENSE operates through differentiable integration within multimodal retrieval settings,and further demonstrates how regulatory signals interact.In extensive experiments spanning three datasets,two scientific benchmarks,guided narrative completion,and factor verification pipelines grounded via Wikidata concepts.

Added

2026-10-02