In order to give machines, the interpretable thinking ability of mathematicians, the automatic derivation engine for advanced mathematics symbolic systems was explored to develop, which could update machines from the shallow thinking ability, such as natural language understanding and elementary mathematical numerical computation, to deep thinking, such as equivalent derivation for symbolic systems. This article proposed the complex logic algorithm design and development method with the frameworks as the core components. Starting with problem-resolving examples, the initial idea, basic data structure, and programming features of this new method were introduced in detail. However, this article proposed the integrated development environment for this method, as well as the main scheduling algorithm, core process algorithm, workflow dynamic display algorithm, execution status monitoring algorithm, generalization processing method, etc. The new method could be applicable to intelligent system development tasks that needed to gradually accumulate instance experience and had practical significance for the complex logic algorithms development, visualization software design, reduction complexity for software test and maintenance, and software reliability improvement. This article used the application problem solved by partial differential equations as an example to explain this method from the whole process, such as lexical analysis, semantic analysis, symbolic system establishment, and equivalent derivation to result validation, demonstrating the new dynamism and potential for logic derivation-based classical artificial intelligence methods.

1. Newcomb A, Kalita J. Explaining Math Word Problem Solvers. In: Proceedings of the 2022 6th International Conference on Natural Language Processing and Information Retrieval; 2022.

2. Qin J, Huang Z, Zeng Y, et al. An Introspective Data Augmentation Method for Training Math Word Problem Solvers. In: IEEE/ACM Transactions on Audio, Speech, and Language Processing; 2024.

3. Paliwal P. Adversarial Analysis and Methods for Math Word Problems. In: Proceedings of the International Conference on Computing, Machine Learning and Data Science. 2024.

4. Zhu P, Lv P, Shi J, et al. Design and implementation of text understanding system based on semantic tagging Instances. In: Proceedings of the 4th International Conference on Artificial Intelligence in Electronics Engineering (AIEE ‘23); 2023.

5. Patel M, Dogan FI, Zeng Z, et al. Semantic scene understanding for human-robot interaction. In: Proceedings of the Companion of the ACM/IEEE International Conference on Human-Robot Interaction (HRI ‘23); 2023.

6. Nguyen TP, Razniewski S, Varde A, and Weikum G. Extracting cultural commonsense knowledge at scale. In: Proceedings of the ACM Web Conference (WWW ‘23); 2023.

7. Iravanian S, Gowda S, Rackauckas C. Hybrid Symbolic-Numeric and Numerically-Assisted Symbolic Integration. In: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation; 2024.

8. Taihei Oki and Yujin Song. Structural preprocessing method for nonlinear differential-algebraic equations using linear symbolic matrices. In: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation (ISSAC ‘24); 2024.

9. Kaltofen EL. Encounters in Symbolic Computation: Ideas for the Ages. In: Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation; 2024.

10. Gewaltig MO. Towards Simulating the Human Brain. In: Proceedings of the 2017 ACM SIGSIM Conference on Principles of Advanced Discrete Simulation; 2017.

11. Meilong C, Xiehua Y, Shaozi L, et al. Design of Graphic Interactive Experimental Platform Based on MATLAB. In: Proceedings of the 2022 12th International Conference on Information Technology in Medicine and Education (ITME); 2022.

12. Valina L, Teixeira B, Reis A, et al. Explainable Artificial Intelligence for Deep Synthetic Data Generation Models. In: Proceedings of the 2024 IEEE Conference on Artificial Intelligence (CAI); 2024.

13. Hickling T, Zenati A, Aouf N, et al. Explainability in Deep Reinforcement Learning: A Review into Current Methods and Applications. ACM Computing Surveys. 2023; 56(5): 1-35. doi: 10.1145/3623377.

14. Ahmed YA, Sharo A. On the education effect of CHATGPT: Is AI CHATGPT to dominate education career profession? In: Proceedings of the 2023 International Conference on Intelligent Computing, Communication, Networking and Services (ICCNS); 2023.

15. Arulmohan S, Meurs MJ, Mosser S. Extracting Domain Models from Textual Requirements in the Era of Large Language Models. In: Proceedings of the 2023 ACM/IEEE International Conference on Model Driven Engineering Languages and Systems Companion (MODELS-C); 2023.

16. Franceschelli G, Musolesi M. Creativity and Machine Learning: A Survey. ACM Computing Surveys. 2024; 56(11): 1-41. doi: 10.1145/3664595

17. Subagdja B, Shanthoshigaa D, Wang Z, et al. Machine Learning for Refining Knowledge Graphs: A Survey. ACM Computing Surveys. 2024; 56(6): 1-38. doi: 10.1145/3640313

18. Seyyedi A, Bohlouli M, Oskoee SN. Machine Learning and Physics: A Survey of Integrated Models. ACM Computing Surveys. 2023; 56(5): 1-33. doi: 10.1145/3611383

19. Brunton SL, Kutz JN. Promising directions of machine learning for partial differential equations. Nature Computational Science. 2024; 4(7): 483-494. doi: 10.1038/s43588-024-00643-2

20. Duan X, Wang X, Zhao P, et al. DeepLogic: Joint Learning of Neural Perception and Logical Reasoning. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2022: 1-14. doi: 10.1109/tpami.2022.3191093

21. Vamplew P, Foale C, Hayes CF, et al. Utility-based reinforcement learning: Unifying single-objective and multi-objective reinforcement learning. In: Proceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS ‘24); 2024.

22. Flageat M, Lim B, Cully A. Evolutionary Reinforcement Learning. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion; 2024.

23. Harada T, Alba E. Parallel Genetic Algorithms. ACM Computing Surveys. 2020; 53(4): 1-39. doi: 10.1145/3400031

24. Zamanzadeh Darban Z, Webb GI, Pan S, et al. Deep Learning for Time Series Anomaly Detection: A Survey. ACM Computing Surveys. 2024; 57(1): 1-42. doi: 10.1145/3691338

25. Wan Y, Bi Z, He Y, et al. Deep Learning for Code Intelligence: Survey, Benchmark and Toolkit. ACM Computing Surveys. 2024; 56(12): 1-41. doi: 10.1145/3664597

26. Wijesekara PADSN, Wang YK. A Mathematical Epidemiological Model (SEQIJRDS) to Recommend Public Health Interventions Related to COVID-19 in Sri Lanka. COVID. 2022; 2(6): 793-826. doi: 10.3390/covid2060059

27. Wijesekara PADSN. Deep 3D Dynamic Object Detection towards Successful and Safe Navigation for Full Autonomous Driving. The Open Transportation Journal. 2022; 16(1). doi: 10.2174/18744478-v16-e2208191

28. Nguyen K, Proença H, Alonso-Fernandez F. Deep Learning for Iris Recognition: A Survey. ACM Computing Surveys. 2024; 56(9): 1-35. doi: 10.1145/3651306

29. Spannaus A, Hanson HA, Tourassi G, et al. Topological Interpretability for Deep Learning. In: Proceedings of the Platform for Advanced Scientific Computing Conference; 2024.

30. Kletsko E, van Rozen R. Advanced Game Engine Wizardry for Visual Programming Environments. In: Proceedings of the 3rd ACM SIGPLAN International Workshop on Programming Abstractions and Interactive Notations, Tools, and Environments; 2024.

31. Homer M. Reclaiming the Unexplored in Hybrid Visual Programming. In: Proceedings of the 2024 ACM SIGPLAN International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software; 2024.

32. Homer M. In-Line Compositional Visual Programming. In: Proceedings of the 8th International Conference on the Art, Science, and Engineering of Programming; 2024.

33. Glock J. Aiding Developer Understanding of Software Changes via Symbolic Execution-based Semantic Differencing. In: Proceedings of the 2024 IEEE/ACM 46th International Conference on Software Engineering: Companion Proceedings; 2024.

34. Krestel R, Aras H, Andersson L, et al. In: Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, Proceedings of the 5th Workshop on Patent Text Mining and Semantic Technologies (PatentSemTech2024); 2024.

35. Huang S, Luan Z. Semantic-Aware Log Understanding and Analysis. In: Proceedings of the 33rd International Symposium on High-Performance Parallel and Distributed Computing; 2024.

36. Fang J, Wang W, Luo T, et al. Progressive Multimodal Pivot Learning: Towards Semantic Discordance Understanding as Humans. In: Proceedings of the 33rd ACM International Conference on Information and Knowledge Management; 2024.

37. D’Aquin M, Bunoiu R, Cirstea H, et al. Combining representation formalisms for reasoning upon mathematical knowledge. In: Proceedings of the 12th Knowledge Capture Conference 2023; 2023.

38. Liu J, Huang Z, Ma Z, et al. Guiding Mathematical Reasoning via Mastering Commonsense Formula Knowledge. In: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining; 2023.

39. Greiner-Petter A, Schubotz M, Müller F, et al. Discovering Mathematical Objects of Interest—A Study of Mathematical Notations. In: Proceedings of The Web Conference 2020; 2020.

40. Zhao WX, Zhou K, Gong Z, et al. JiuZhang: A Chinese Pre-trained Language Model for Mathematical Problem Understanding. In: Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining; 2022.

41. Xu J, Fei H, Pan L, et al. Faithful logical reasoning via symbolic chain-of-thought. Available online: https://arxiv.org/pdf/2405.18357.pdf (accessed on 1 May 2024).