Learning and Reasoning Over Time: Challenges, Evaluation, and Opportunities

Neuro-symbolic Artificial Intelligence aims to bridge the gap between Machine Learning and Classic Artificial Intelligence, by integrating Learning and Reasoning within a unified framework. In this thesis we focus on two of the challenges in Neuro-symbolic integration, with a particular emphasis on the role of Time: (i.) learning symbolic representations, and (ii.) benchmarking Neuro-symbolic systems in a coherent and reproducible fashion. We describe desirable properties of symbolic representations and propose a novel taxonomy for benchmarks in Neuro-symbolic Artificial Intelligence, which we believe can harmonize existing benchmarks into coherent evaluation suites, and promote the development of novel frameworks covering currently under-explored niches. We propose two novel fully-customizable benchmarking frameworks with a strong temporal component. KANDY is a Curriculum-based Abstract Visual Reasoning framework for Inductive Learning and Hierarchical Concept Discovery, which exploits time to present tasks of increasing complexity to a learning agent. LTLZinc is a Constraint-based Learning and Reasoning over Time formalism and evaluation framework, capable of generating novel tasks relevant for the Temporal Reasoning and Continual Learning communities. Experiments on KANDY highlight the importance of time in both guiding the reasoning process, and promoting the autonomous development of novel concepts. In spite of its perceptual simplicity, KANDY is challenging for Neural Networks, Symbolic methods and Vision Language Models, and the exploitation of its curricular nature is fundamental to overcome some of the reasoning challenges it poses. We also developed a novel Concept-based approach exploiting Symbolic Representation Learning and the curricular progression of KANDY to develop task-driven concepts without providing explicit supervisions. LTLZinc is capable of generating tasks of interest for the Temporal Reasoning community which are both extensions of existing settings (Sequence Classification with Relational Background Knowledge), and novel settings (Constraint Induction over Time, and Temporal Distant Supervision). Our experiments on Sequence Classification highlight the challenging nature of a relational setting and open up to the possibility of Approximate Formal Verification of Safety-Critical Systems by Neuro-symbolic means. LTLZinc extends the Incremental Learning framework to a broader class of Continual Learning problems, which is both more expressive from a temporal perspective, and characterized by the possibility of injecting temporal knowledge to counteract catastrophic forgetting. Our experiments point toward the necessity of more sophisticated Continual Learning methods capable of exploiting temporal knowledge effectively.