{"type":"ScholarlyArticle","title":"Deep Symbolic Learning: Discovering Symbols and Rules from Perceptions","authors":[{"name":"Alessandro Daniele","slug":"alessandro-daniele","given":"Alessandro","family":"Daniele","affiliation":"Fondazione Bruno Kessler , Trento , Italy,"},{"name":"Tommaso Campari","slug":"tommaso-campari","given":"Tommaso","family":"Campari","affiliation":"Fondazione Bruno Kessler , Trento , Italy,; Università degli Studi di Padova , Italy"},{"name":"Sagar Malhotra","slug":"sagar-malhotra","given":"Sagar","family":"Malhotra","affiliation":"Fondazione Bruno Kessler , Trento , Italy,; TU Wien , Austria"},{"name":"Luciano Serafini","slug":"luciano-serafini","given":"Luciano","family":"Serafini","affiliation":"Fondazione Bruno Kessler , Trento , Italy,"}],"abstract":"Neuro-Symbolic (NeSy) integration combines symbolic reasoning with Neural Networks (NNs) for tasks requiring perception and reasoning. Most NeSy systems rely on continuous relaxation of logical knowledge, and no discrete decisions are made within the model pipeline. Furthermore, these methods assume that the symbolic rules are given. In this paper, we propose Deep Symboilic Learning (DSL), a NeSy system that learns NeSy-functions, i.e., the composition of a (set of) perception functions which map continuous data to discrete symbols, and a symbolic function over the set of symbols. DSL simultaneously learns the perception and symbolic functions while being trained only on their composition (NeSy-function). The key novelty of DSL is that it can create internal (interpretable) symbolic representations and map them to perception inputs within a differentiable NN learning pipeline. The created symbols are automatically selected to generate symbolic functions that best explain the data. We provide experimental analysis to substantiate the efficacy of DSL  in simultaneously learning perception and symbolic functions.","doi":"10.24963/ijcai.2023/400","url":"https://ijcai.org/proceedings/2023/400","pdf":"https://ijcai.org/proceedings/2023/0400.pdf","markdown":"https://ijcai.org/proceedings/2023/400.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/400","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Machine Learning","track":"Main Track","number":400,"pages":{"first":3597,"last":3605},"keywords":["Knowledge Representation and Reasoning: KRR: Learning and reasoning","Machine Learning: ML: Explainable/Interpretable machine learning","Machine Learning: ML: Neuro-symbolic methods"],"videos":[],"references":[{"position":1,"raw":"[Aspis et al., 2022] Yaniv Aspis, Krysia Broda, Jorge Lobo, and Alessandra Russo. 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