The integration of deep learning and logic reasoning is still an open-research problem and it is considered to be the key for the development of real intelligent agents. From one side, deep learning obtained amazing results in many fields of artificial intelligence like computer vision, natural language processing and so on. On the other hand, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference.

Research directions

First-Order Logic (FOL) formulas have been shown to suitably express the available knowledge to define a certain learning problem, in particular in multi-task classification problems where a set of unknown (task) functions have to be learnt. In this framework, the logical formulas may be converted into differentiable functions by means of a chosen t-norm fuzzy logic. The task functions can be considered as logical predicates and are generally implemented as (deep) multi-layer perceptrons. This allows us from one side to exploit state-of-the-art deep architectures and on the other hand to embed interpretable symbolic relations among the task functions in the optimization problem.

In the following are reported the main topics that are still under investigation, together with some references from the key publication list.

• Integrating Leaning and Reasoning with Deep Logic Models
  Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2019). Integrating Learning and Reasoning with Deep Logic Models. arXiv preprint arXiv:1901.04195.
• Loss functions and t-norm generators
  Marra, G., Giannini, F., Diligenti, M., Maggini, M., & Gori, M. (2019). Learning and T-Norms Theory. arXiv preprint arXiv:1907.11468.
• Convex logical constraints
  Giannini, F., Diligenti, M., Gori, M., & Maggini, M. (2018). On a convex logic fragment for learning and reasoning. IEEE Transactions on Fuzzy Systems.

Talks

• LYRICS: a unified framework for learning and inference with constraints – IDA – Czech Technical University – Prague – January 2019
• Integrating deep learning and reasoning with First Order Fuzzy Logic – DTAI – KU Leuven – Leuven – September 2018
• Characterization of the Convex Łukasiewicz Fragment for Learning from Constraints, AAAI2018, New Orleans, USA, January 2018
• Learning Łukasiewicz Logic Fragments by Quadratic Programming, ECML-PKDD2017, Skopje, Macedonia, September 2017
• Learning from Logical Constraints by Quadratic Optimization, Fondazione Bruno Kessler FBK, Trento, June 2017

Key Publications

• Marra, G., Giannini, F., Diligenti, M., Maggini, M., & Gori, M. (2019). Learning and T-Norms Theory. arXiv preprint arXiv:1907.11468. (submitted to TNNLS)
• Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2019). LYRICS: a General Interface Layer to Integrate Logic and Deep Learning. arXiv preprint arXiv:1903.07534. (to appear in ECML 2019)
• Marra, G., Giannini, F., Diligenti, M., & Gori, M. (2019). Integrating Learning and Reasoning with Deep Logic Models. arXiv preprint arXiv:1901.04195. (to appear in ECML 2019)
• Teso, S., Masera, L., Diligenti, M., & Passerini, A. (2019). Combining learning and constraints for genome-wide protein annotation. BMC bioinformatics, 20(1), 338.
• Graziani, L., Melacci, S., & Gori, M. (2019). Coherence constraints in facial expression recognition. Intelligenza Artificiale, 13(1), 79-92.
• Giannini, F., Diligenti, M., Gori, M., & Maggini, M. (2018). On a convex logic fragment for learning and reasoning. IEEE Transactions on Fuzzy Systems.
• Zugarini, A., Morvan, J., Melacci, S., Knerr, S., & Gori, M. (2018, September). Combining deep learning and symbolic processing for extracting knowledge from raw text. In IAPR Workshop on Artificial Neural Networks in Pattern Recognition (pp. 90-101). Springer, Cham.
• Roychowdhury, S., Diligenti, M., & Gori, M. (2018, June). Image Classification Using Deep Learning and Prior Knowledge. In Workshops at the Thirty-Second AAAI Conference on Artificial Intelligence.
• Diligenti, M., Gori, M., & Sacca, C. (2017). Semantic-based regularization for learning and inference. Artificial Intelligence, 244, 143-165.
• Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti: ” Foundations of Support Constraint Machines “. Neural Computation (MIT Press), 2015