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Heuristic Backward Chaining Based on Predicate Tensorization

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Artificial Intelligence in Intelligent Systems (CSOC 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 229))

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Abstract

Inference methods for first-order logic or its fragments are inherently slow. Neural networks make it possible to rapidly approximate the truth values of ground atoms but the results are not explainable and not necessarily accurate. A hybrid neural-symbolic inference method is proposed in this paper. It is a framework for incorporating predicate tensorization techniques into backward chaining and its extensions. Heuristic functions for best-first search strategies for backward chaining are defined via tensor representations of predicates. These strategies speed up inference by reducing backtracking.

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References

  1. Chang, C.L., Lee, R.C.T.: Symbolic Logic and Mechanical Theorem Proving. Academic press, Cambridge (1973)

    Google Scholar 

  2. Chen, R., Gotsman, C.: Efficient fastest-path computations in road maps. arXiv preprint arXiv:1810.01776 (2018)

  3. Cingillioglu, N., Russo, A.: DeepLogic: towards end-to-end differentiable logical reasoning. In: AAAI 2019 Spring Symposium on Combining Machine Learning with Knowledge Engineering, vol. 2350. CEUR-WS.org (2019)

    Google Scholar 

  4. Cohen, W., Yang, F., Mazaitis, K.R.: Tensorlog: a probabilistic database implemented using deep-learning infrastructure. J. Artif. Intell. Res. 67, 285–325 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dong, H., Mao, J., Lin, T., Wang, C., Li, L., Zhou, D.: Neural logic machines. In: International Conference on Learning Representations (2019)

    Google Scholar 

  6. d’Avila Garcez, A.S., Gori, M., Lamb, L.C., Serafini, L., Spranger, M., Tran, S.N.: Neural-symbolic computing: an effective methodology for principled integration of machine learning and reasoning. J. Appl. Logics 6(4), 611–632 (2019)

    MathSciNet  MATH  Google Scholar 

  7. Kimmig, A., Demoen, B., De Raedt, L., Costa, V.S., Rocha, R.: On the implementation of the probabilistic logic programming language ProbLog. arXiv preprint arXiv:1006.4442 (2010)

  8. Knuth, D.E.: Art of Programming, vol. 2: Seminumerical Algorithms, vol. 2. Addison-Wesley, Boston (1998)

    Google Scholar 

  9. Lamb, L.C., d’Avila Garcez, A.S., Gori, M., Prates, M.O.R., Avelar, P.H.C., Vardi, M.Y.: Graph neural networks meet neural-symbolic computing: a survey and perspective. In: Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, pp. 4877–4884 (2020)

    Google Scholar 

  10. Manhaeve, R., Dumancic, S., Kimmig, A., Demeester, T., De Raedt, L.: DeepProbLog: neural probabilistic logic programming. In: Advances in Neural Information Processing Systems, pp. 3749–3759 (2018)

    Google Scholar 

  11. Marcus, G.: The next decade in AI: four steps towards robust artificial intelligence. arXiv preprint arXiv:2002.06177 (2020)

  12. Marra, G., Giannini, F., Diligenti, M., Gori, M.: Integrating learning and reasoning with deep logic models. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases, pp. 517–532 (2019)

    Google Scholar 

  13. McCune, W.: Otter 3.3 reference manual and guide. Technical report, Argonne National Laboratory (2003)

    Google Scholar 

  14. Minervini, P., Bosnjak, M., Rocktäschel, T., Riedel, S., Grefenstette, E.: Differentiable reasoning on large knowledge bases and natural language. In: Knowledge Graphs for eXplainable Artificial Intelligence: Foundations, Applications and Challenges, pp. 125–142. IOS Press (2020)

    Google Scholar 

  15. Nilsson, N.J.: Principles of Artificial Intelligence. Morgan Kaufmann, Massachusetts (2014)

    Google Scholar 

  16. Rocktäschel, T.: Combining representation learning with logic for language processing. CoRR (2017). http://arxiv.org/abs/1712.09687

  17. Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice Hall Press, 3rd edn. (2009)

    Google Scholar 

  18. Sakharov, A.: Hierarchical rules for knowledge representation and learning. In: IEEE 2nd International Conference on Artificial Intelligence and Knowledge Engineering, pp. 167–171 (2019)

    Google Scholar 

  19. Sakharov, A.: Hierarchical resolution for structured predicate definitions. In: 11th Hellenic Conference on Artificial Intelligence, pp. 202–210 (2020)

    Google Scholar 

  20. Sakharov, A.: A best-first backward-chaining search strategy based on learned predicate representations. In: 13th International Conference on Agents and Artificial Intelligence, vol. 2, pp. 982–989 (2021)

    Google Scholar 

  21. Serafini, L., d’Avila Garcez, A.S.: Logic tensor networks: deep learning and logical reasoning from data and knowledge. In: 11th International Workshop on Neural-Symbolic Learning and Reasoning, vol. 1768. CEUR-WS.org (2016)

    Google Scholar 

  22. Shen, Y.D., Yuan, L.Y., You, J.H.: Loop checks for logic programs with functions. Theor. Comput. Sci. 266(1–2), 441–461 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Stickel, M.E.: A Prolog technology theorem prover: a new exposition and implementation in Prolog. Theor. Comput. Sci. 104(1), 109–128 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  24. Swift, T.: Design patterns for tabled logic programming. In: Abreu, S., Seipel, D. (eds.) Applications of Declarative Programming and Knowledge Management. INAP 2009. Lecture Notes in Computer Science, vol. 6547, pp. 1–19. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-20589-7_1

  25. Van Krieken, E., Acar, E., Van Harmelen, F.: Semi-supervised learning using differentiable reasoning. J. Appl. Logics 6(4), 633–651 (2019)

    MathSciNet  MATH  Google Scholar 

  26. Zhang, Y., et al.: Efficient probabilistic logic reasoning with graph neural networks. In: International Conference on Learning Representations (2020)

    Google Scholar 

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Authors and Affiliations

  1. Synstretch, Framingham, MA, USA

    Alexander Sakharov

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  1. Alexander Sakharov
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Correspondence to Alexander Sakharov .

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Editors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic

    Radek Silhavy

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Sakharov, A. (2021). Heuristic Backward Chaining Based on Predicate Tensorization. In: Silhavy, R. (eds) Artificial Intelligence in Intelligent Systems. CSOC 2021. Lecture Notes in Networks and Systems, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-77445-5_52

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