An Admissibility-Theoretic Taxonomy of AI Capability Levels: From Narrow AI to Artificial Superintelligence
Author
Ian Staley
Abstract
Current taxonomies of artificial intelligence capability, running from narrow AI through artificial general intelligence (AGI) to artificial superintelligence (ASI), are overwhelmingly behavioral: they define levels by what systems can be observed to do. This approach faces well-documented coherence problems at the AGI/ASI boundary, where behavioral signatures underdetermine the type of system under examination, definitions drift with each model release, and disagreements resist empirical resolution. This paper proposes a non-behavioral alternative: an admissibility-theoretic taxonomy in which capability levels are characterized not by observed outputs but by the structure of admissible trajectories through capability space, with structural inspiration drawn from final-state-constrained formalisms in physics and information theory. The framework defines narrow AI as the regime in which admissible histories are bounded by externally specified terminal conditions, AGI as the regime in which terminal conditions become endogenously selected, and ASI as the regime in which the system modifies its own admissibility criteria. It gives a formal handle on whether transitions between levels are continuous or phase-transitional, clarifies how behavioral benchmarks can mistake narrow capability scaling for general capability emergence, and supplies vocabulary for instrumental convergence and mesa-optimization. The borrowing is structural rather than literal: no quantum mechanism is claimed.
Keywords
artificial general intelligence; artificial superintelligence; capability taxonomy; admissible histories; final-state constraints.
Full Text:
References
- Aharonov, Y., Bergmann, P. G., & Lebowitz, J. L. (1964). Time symmetry in the quantum process of measurement. Physical Review, 134(6B), B1410-B1416. https://doi.org/10.1103/PhysRev.134.B1410
- Aharonov, Y., & Vaidman, L. (2008). The two-state vector formalism: An updated review. In J. G. Muga, R. Sala Mayato, & I. L. Egusquiza (Eds.), Time in quantum mechanics(Lecture Notes in Physics, Vol. 734, pp. 399-447). Springer. https://doi.org/10.1007/978-3-540-73473-4_13
- Anbar Jafari, A., Ozcinar, C., & Anbarjafari, G. (2025). A mathematical framework for AI singularity: Conditions, bounds, and control of recursive improvement. https://doi.org/10.48550/arXiv.2511.10668
- Bai, Y., Kadavath, S., Kundu, S., et al. (2022). Constitutional AI: Harmlessness from AI feedback. https://doi.org/10.48550/arXiv.2212.08073
- Bender, E. M., Gebru, T., McMillan-Major, A., & Shmitchell, S. (2021). On the dangers of stochastic parrots: Can language models be too big? In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency(pp. 610-623). Association for Computing Machinery. https://doi.org/10.1145/3442188.3445922
- Bennett, M. T. (2025). Quantum AGI: Ontological foundations. https://doi.org/10.48550/arXiv.2506.13134
- Blili-Hamelin, B., Graziul, C., Hancox-Li, L., Hazan, H., El-Mhamdi, E.-M., Ghosh, A., Heller, K., Metcalf, J., Murai, F., Salvaggio, E., Smart, A., Snider, T., Tighanimine, M., Ringer, T., Mitchell, M., & Dori-Hacohen, S. (2025). Stop treating 'AGI' as the north-star goal of AI research. In Proceedings of the 42nd International Conference on Machine Learning(Position Paper Track). https://doi.org/10.48550/arXiv.2502.03689
- Bostrom, N. (2014). Superintelligence: Paths, dangers, strategies.Oxford University Press.
- Bowman, S. R., Hyun, J., Perez, E., et al. (2022). Measuring progress on scalable oversight for large language models. https://doi.org/10.48550/arXiv.2211.03540
- Bubeck, S., Chandrasekaran, V., Eldan, R., Gehrke, J., Horvitz, E., Kamar, E., Lee, P., Lee, Y. T., Li, Y., Lundberg, S., Nori, H., Palangi, H., Ribeiro, M. T., & Zhang, Y. (2023). Sparks of artificial general intelligence: Early experiments with GPT-4. https://doi.org/10.48550/arXiv.2303.12712
- Carlsmith, J. (2022). Is power-seeking AI an existential risk? https://doi.org/10.48550/arXiv.2206.13353
- Chaitin, G. J. (1966). On the length of programs for computing finite binary sequences. Journal of the ACM, 13(4), 547-569. https://doi.org/10.1145/321356.321363
- Chen, M., Tworek, J., Jun, H., et al. (2021). Evaluating large language models trained on code. https://doi.org/10.48550/arXiv.2107.03374
- Chollet, F. (2019). On the measure of intelligence. https://doi.org/10.48550/arXiv.1911.01547
- Cover, T. M., & Thomas, J. A. (2006). Elements of information theory(2nd ed.). Wiley-Interscience. https://doi.org/10.1002/047174882X
- Dennett, D. C. (1987). The intentional stance.MIT Press.
- Floridi, L., & Sanders, J. W. (2004). On the morality of artificial agents. Minds and Machines, 14(3), 349-379. https://doi.org/10.1023/B:MIND.0000035461.63578.9d
- Friston, K. J. (2010). The free-energy principle: A unified brain theory? Nature Reviews Neuroscience, 11, 127-138. https://doi.org/10.1038/nrn2787
- Friston, K., FitzGerald, T., Rigoli, F., Schwartenbeck, P., & Pezzulo, G. (2017). Active inference: A process theory. Neural Computation, 29(1), 1-49. https://doi.org/10.1162/NECO_a_00912
- Gell-Mann, M., & Hartle, J. B. (1990). Quantum mechanics in the light of quantum cosmology. In W. H. Zurek (Ed.), Complexity, entropy, and the physics of information(pp. 425-458). Addison-Wesley.
- Goertzel, B. (2021). The general theory of general intelligence: A pragmatic patternist perspective. Journal of Artificial General Intelligence.https://doi.org/10.48550/arXiv.2103.15100
- Goertzel, B. (2024). Metagoals endowing self-modifying AGI systems with goal stability or moderated goal evolution: Toward a formally sound and practical approach. https://doi.org/10.48550/arXiv.2412.16559
- Goertzel, B., & Pennachin, C. (Eds.). (2007). Artificial general intelligence(Cognitive Technologies). Springer. https://doi.org/10.1007/978-3-540-68677-4
- Good, I. J. (1965). Speculations concerning the first ultraintelligent machine. Advances in Computers, 6, 31-88. https://doi.org/10.1016/S0065-2458(08)60418-0
- Griffiths, R. B. (1984). Consistent histories and the interpretation of quantum mechanics. Journal of Statistical Physics, 36(1-2), 219-272. https://doi.org/10.1007/BF01015734
- Griffiths, R. B. (2002). Consistent quantum theory.Cambridge University Press. https://doi.org/10.1017/CBO9780511606052
- Halliwell, J. J. (1995). A review of the decoherent histories approach to quantum mechanics. Annals of the New York Academy of Sciences, 755, 726-740. https://doi.org/10.1111/j.1749-6632.1995.tb39017.x
- Hartle, J. B., & Hawking, S. W. (1983). Wave function of the universe. Physical Review D, 28(12), 2960-2975. https://doi.org/10.1103/PhysRevD.28.2960
- Hendrycks, D., Burns, C., Basart, S., Zou, A., Mazeika, M., Song, D., & Steinhardt, J. (2021). Measuring massive multitask language understanding. In Proceedings of the International Conference on Learning Representations.https://doi.org/10.48550/arXiv.2009.03300
- Hernandez-Orallo, J. (2017). The measure of all minds: Evaluating natural and artificial intelligence.Cambridge University Press. https://doi.org/10.1017/9781316594179
- Hubinger, E., van Merwijk, C., Mikulik, V., Skalse, J., & Garrabrant, S. (2019). Risks from learned optimization in advanced machine learning systems. https://doi.org/10.48550/arXiv.1906.01820
- Irving, G., Christiano, P., & Amodei, D. (2018). AI safety via debate. https://doi.org/10.48550/arXiv.1805.00899
- Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information. Problems of Information Transmission, 1(1), 1-7.
- Lake, B. M., Ullman, T. D., Tenenbaum, J. B., & Gershman, S. J. (2017). Building machines that learn and think like people. Behavioral and Brain Sciences, 40, e253. https://doi.org/10.1017/S0140525X16001837
- Legg, S., & Hutter, M. (2007). Universal intelligence: A definition of machine intelligence. Minds and Machines, 17(4), 391-444. https://doi.org/10.1007/s11023-007-9079-x
- Li, M., & Vitanyi, P. M. B. (2019). An introduction to Kolmogorov complexity and its applications(4th ed.). Springer. https://doi.org/10.1007/978-3-030-11298-1
- Marletto, C., & Vedral, V. (2017). Evolution without evolution and without ambiguities. Physical Review D, 95, 043510. https://doi.org/10.1103/PhysRevD.95.043510
- Metz, R. (2024, July 11). OpenAI sets levels to track progress toward superintelligent AI. Bloomberg News.
- Mitchell, M. (2024). Debates on the nature of artificial general intelligence. Science, 383(6689), eado7069. https://doi.org/10.1126/science.ado7069
- Mitchell, M., & Krakauer, D. C. (2023). The debate over understanding in AI's large language models. Proceedings of the National Academy of Sciences, 120(13), e2215907120. https://doi.org/10.1073/pnas.2215907120
- Morris, M. R., Sohl-Dickstein, J., Fiedel, N., Warkentin, T., Dafoe, A., Faust, A., Farabet, C., & Legg, S. (2024). Levels of AGI for operationalizing progress on the path to AGI. In Proceedings of the 41st International Conference on Machine Learning(Vol. 235). https://doi.org/10.48550/arXiv.2311.02462
- Ngo, R., Chan, L., & Mindermann, S. (2024). The alignment problem from a deep learning perspective. In Proceedings of the International Conference on Learning Representations.https://doi.org/10.48550/arXiv.2209.00626
- Omnes, R. (1994). The interpretation of quantum mechanics.Princeton University Press.
- Omohundro, S. M. (2008). The basic AI drives. In P. Wang, B. Goertzel, & S. Franklin (Eds.), Proceedings of the First Conference on Artificial General Intelligence(Frontiers in Artificial Intelligence and Applications, Vol. 171, pp. 483-492). IOS Press.
- Ouyang, L., Wu, J., Jiang, X., Almeida, D., Wainwright, C. L., Mishkin, P., Zhang, C., Agarwal, S., Slama, K., Ray, A., Schulman, J., Hilton, J., Kelton, F., Miller, L., Simens, M., Askell, A., Welinder, P., Christiano, P., Leike, J., & Lowe, R. (2022). Training language models to follow instructions with human feedback. In Advances in Neural Information Processing Systems(Vol. 35). https://doi.org/10.48550/arXiv.2203.02155
- Page, D. N., & Wootters, W. K. (1983). Evolution without evolution: Dynamics described by stationary observables. Physical Review D, 27(12), 2885-2892. https://doi.org/10.1103/PhysRevD.27.2885
- Parr, T., Pezzulo, G., & Friston, K. J. (2022). Active inference: The free energy principle in mind, brain, and behavior.MIT Press.
- Pfister, R., & Jud, H. (2025). Understanding and benchmarking artificial intelligence: OpenAI's o3 is not AGI. https://doi.org/10.48550/arXiv.2501.07458
- Power, A., Burda, Y., Edwards, H., Babuschkin, I., & Misra, V. (2022). Grokking: Generalization beyond overfitting on small algorithmic datasets. https://doi.org/10.48550/arXiv.2201.02177
- Rein, D., Hou, B. L., Stickland, A. C., Petty, J., Pang, R. Y., Dirani, J., Michael, J., & Bowman, S. R. (2023). GPQA: A graduate-level Google-proof Q&A benchmark. https://doi.org/10.48550/arXiv.2311.12022
- Russell, S. (2019). Human compatible: Artificial intelligence and the problem of control.
- Schaeffer, R., Miranda, B., & Koyejo, S. (2023). Are emergent abilities of large language models a mirage? In Advances in Neural Information Processing Systems(Vol. 36). https://doi.org/10.48550/arXiv.2304.15004
- Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423; 27(4), 623-656. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
- Solomonoff, R. J. (1964). A formal theory of inductive inference, Parts I and II. Information and Control, 7(1), 1-22; 7(2), 224-254. https://doi.org/10.1016/S0019-9958(64)90223-2
- Sommers, P. (1994). The role of the future in quantum theory. https://doi.org/10.48550/arXiv.gr-qc/9404022
- Srivastava, A., Rastogi, A., Rao, A., et al. (2023). Beyond the imitation game: Quantifying and extrapolating the capabilities of language models. Transactions on Machine Learning Research.https://doi.org/10.48550/arXiv.2206.04615
- Staley, I. (2026). Final-state constraints and informational pruning in quantum histories. International Journal of Quantum Foundations, 12(2), 719-737. https://doi.org/10.5281/zenodo.19512844
- Vaidman, L. (2009). Two-state vector formalism. In D. Greenberger, K. Hentschel, & F. Weinert (Eds.), Compendium of quantum physics(pp. 802-805). Springer. https://doi.org/10.1007/978-3-540-70626-7_237
- Wang, P., & Goertzel, B. (Eds.). (2012). Theoretical foundations of artificial general intelligence(Atlantis Thinking Machines, Vol. 4). Atlantis Press. https://doi.org/10.2991/978-94-91216-62-6
- Wei, J., Tay, Y., Bommasani, R., Raffel, C., Zoph, B., Borgeaud, S., Yogatama, D., Bosma, M., Zhou, D., Metzler, D., Chi, E. H., Hashimoto, T., Vinyals, O., Liang, P., Dean, J., & Fedus, W. (2022). Emergent abilities of large language models. Transactions on Machine Learning Research.https://doi.org/10.48550/arXiv.2206.07682
- Yudkowsky, E. (2013). Intelligence explosion microeconomics(Technical Report). Machine Intelligence Research Institute.