What does it mathematically mean for an AI-generated claim to be "true", "justified", and "trustworthy"?

Overview

I'm working on a research project, the end goal of which is not to create a better LLM, but rather to create a verification engine that can reason about whether an AI claim is trustworthy enough for a particular application. Most of the current research focuses on making AI "better", I want to tackle the verification side of things. The question I'm asking myself is: What does it mean for a claim to be "true", "justified", and "trustworthy"? I'

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