The integration of deep learning and logic reasoning is still an openresearch 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 higherlevel symbolic inference.
Research directions
FirstOrder Logic (FOL) formulas have been shown to suitably express the available knowledge to define a certain learning problem, in particular in multitask 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 tnorm fuzzy logic. The task functions can be considered as logical predicates and are generally implemented as (deep) multilayer perceptrons. This allows us from one side to exploit stateoftheart 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 tnorm generators
Marra, G., Giannini, F., Diligenti, M., Maggini, M., & Gori, M. (2019). Learning and TNorms 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, ECMLPKDD2017, 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 TNorms 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 genomewide protein annotation. BMC bioinformatics, 20(1), 338.

Graziani, L., Melacci, S., & Gori, M. (2019). Coherence constraints in facial expression recognition. Intelligenza Artificiale, 13(1), 7992.
 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. 90101). Springer, Cham.

Roychowdhury, S., Diligenti, M., & Gori, M. (2018, June). Image Classification Using Deep Learning and Prior Knowledge. In Workshops at the ThirtySecond AAAI Conference on Artificial Intelligence.

Diligenti, M., Gori, M., & Sacca, C. (2017). Semanticbased regularization for learning and inference. Artificial Intelligence, 244, 143165.
 Giorgio Gnecco, Marco Gori, Stefano Melacci, Marcello Sanguineti: ” Foundations of Support Constraint Machines “. Neural Computation (MIT Press), 2015