# On Formally Undecidable Traits of Intelligent Machines

arXiv: https://arxiv.org/abs/2402.09500 · HTML: https://mlsanity.com/paper/2402.09500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 64 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 10 of 10)

- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [Compute Trends Across Three Eras of Machine Learning](https://mlsanity.com/paper/2202.05924/) (2022)
- [Thousands of AI Authors on the Future of AI](https://mlsanity.com/paper/2401.02843/) (2024)
- [New Era of Artificial Intelligence in Education: Towards a Sustainable Multifaceted Revolution](https://mlsanity.com/paper/2305.18303/) (2023)
- [Superintelligence cannot be contained: Lessons from Computability Theory](https://mlsanity.com/paper/1607.00913/) (2016)
- [AI Risk Skepticism, A Comprehensive Survey](https://mlsanity.com/paper/2303.03885/) (2023)
- [Artificial Intelligence for Smart Transportation](https://mlsanity.com/paper/2308.07457/) (2023)

## Abstract (arXiv)

Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism like -- but mathematically distinct from -- the theory of formal languages and their properties. Our formalism affords a precise means for not only talking about the traits we desire of machines (such as them being intelligent, contained, moral, and so forth), but also for detailing the conditions necessary for it to be logically possible to decide whether a given arbitrary machine possesses such a trait or not. Contrary to Alfonseca et al.'s (2021) results, we find that Rice's theorem from computability theory cannot in general be used to determine whether an arbitrary machine possesses a given trait or not. Therefore, it is not necessarily the case that deciding whether an arbitrary machine is intelligent, contained, moral, and so forth is logically impossible.