Formal calculus for self-learning machines

М. Joudakizadeh; А. Beltiukov

Информационные технологии интеллектуальной поддержки принятия решений, Информационные технологии интеллектуальной поддержки принятия решений 2024

М. Joudakizadeh, А. Beltiukov

Изменена: 2025-02-28

Аннотация

This paper introduces a novel weak formal calculus designed for integration into machine learning systems to enhance logical inference capabilities. The proposed calculus operates on a restricted class of formulas, allowing for potential polynomial-time solvability under certain conditions. Our approach bridges the gap between the flexibility of neural networks and the rigor of logical reasoning systems, addressing key challenges in interpretability, generalization, and the incorporation of domain knowledge. The calculus is constructed to be compatible with gradient-based learning algorithms, enabling the optimization of inference strategies through techniques such as deep learning and reinforcement learning. We present the formal properties of the calculus, discuss its potential applications in automated theorem proving and decision-making under uncertainty, and explore integration strategies with neural architectures. This work contributes to the growing field of .more robust, interpretable, and generalizable artificial intelligence systems capable of complex logical reasoning tasks.

Ключевые слова

Artificial Intelligence; Formal Calculus; Machine Learning; Logical Inference; Neuro-Symbolic AI; Interpretable AI; Automated Reasoning

Литература

1. LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. nature, 521(7553), 436-444.

2. Garcez, A. D. A., Gori, M., Lamb, L. C., Serafini, L., Spranger, M., & Tran, S. N. (2019). Neuralsymbolic computing: An effective methodology for principled integration of machine learning and reasoning. arXiv preprint arXiv:1905.06088.

3. Doshi-Velez, F., & Kim, B. (2017). Towards a rigorous science of interpretable machine learning. arXiv preprint arXiv:1702.08608.

4. Marcus, G. (2018). Deep learning: A critical appraisal. arXiv preprint arXiv:1801.00631.

5. Xu, J., Zhang, Z., Friedman, T., Liang, Y., & Broeck, G. (2018, July). A semantic loss function for deep learning with symbolic knowledge. In International conference on machine learning(pp. 5502-5511). PMLR.

6. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on information theory, 52(4), 1289-1306.

7. Wang, P. W., Donti, P., Wilder, B., & Kolter, Z. (2019, May). Satnet: Bridging deep learning and X Международная научная конференция "Информационные технологии интеллектуальной поддержки принятия решений" Уфа-Баку-Чандигарх, 2024 255 logical reasoning using a differentiable satisfiability solver. In International Conference on Machine Learning (pp. 6545-6554). PMLR.

8. Richardson, M., & Domingos, P. (2006). Markov logic networks. Machine learning, 62, 107- 136.

9. Besold, T. R., d’Avila Garcez, A., Bader, S., Bowman, H., Domingos, P., Hitzler, P., ... & Zaverucha, G. (2021). Neural-symbolic learning and reasoning: A survey and interpretation 1. In Neuro-Symbolic Artificial Intelligence: The State of the Art(pp. 1-51). IOS press.

10. Evans, R., & Grefenstette, E. (2018). Learning explanatory rules from noisy data. Journal of Artificial Intelligence Research, 61, 1-64.

11. Urban, J., Sutcliffe, G., Pudlák, P., & Vyskočil, J. (2008, August). MaLARea SG1-machine learner for automated reasoning with semantic guidance. In International Joint Conference on Automated Reasoning (pp. 441-456). Berlin, Heidelberg: Springer Berlin Heidelberg.

12. Kaliszyk, C., Urban, J., Michalewski, H., & Olšák, M. (2018). Reinforcement learning of theorem proving. Advances in Neural Information Processing Systems, 31.

13. Rudin, C. (2019). Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nature machine intelligence, 1(5), 206-215.

14. Richardson, M., & Domingos, P. (2006). Markov logic networks. Machine learning, 62, 107- 136.

15. De Raedt, L., Kimmig, A., & Toivonen, H. (2007, January). Problog: A probabilistic prolog and its application in link discovery. In IJCAI (Vol. 7, pp. 2462-2467).

16. Selsam, D., Lamm, M., Bünz, B., Liang, P., de Moura, L., & Dill, D. L. (2018). Learning a SAT solver from single-bit supervision. arXiv preprint arXiv:1802.03685.

17. Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., ... & Hassabis, D. (2018). A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 362(6419), 1140-1144.

18. Battaglia, P. W., Hamrick, J. B., Bapst, V., Sanchez-Gonzalez, A., Zambaldi, V., Malinowski, M., ... & Pascanu, R. (2018). Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261.