Making AI pervasive requires a holistic approach that covers multiple scales, dimensions, time horizons and data sources. The overall purpose is to support human decision-making in diverse and complex applications, where intelligence starts from low-level signal processing, to middle-level edge AI to higher-level optimization and reasoning in a unified, evidence-based, transparent and holistic approach. Pervasivity requires facing multiple challenges along the following lines: (Q1) How to adapt to diverse environments, to diverse computational and storage resources, and how to cope with real-time vs strategic decision making. (Q2) Being pervasive AI a ubiquitous technology that can be applied to different endeavors and applications in AI that have been traditionally managed by human experts, How to cope with and integrate seamlessly data-driven and knowledge-based approaches. (Q3) From the data-driven perspective, we investigate how to deal with multimodal data, namely images and video, texts, numeric data and IoT signals, both for their comprehension (for classification, segmentation, understanding), and for generation (for prediction, data augmentation and generative learning). To answer these challenges we plan to experiment with the developed foundational research on three main sectors: society with use cases on smart cities (Bologna digital twin) and personalized medicine; economy with use cases on industry 5.0 and finance/banking and culture with use cases on Cultural and software heritage, education and humanistic AI and music. The methodology behind pervasive AI systems is based on multi-modal data analytics, multi-level learning and inference, integration of data-driven and knowledge-based approaches for decision making, in domains where uncertainty is a crucial aspect. These methodological challenges pertain to reasoning, learning, optimization, in presence of uncertainty (Q2 and Q3), multiple sources of information and possibly, scarce computing resources. We aim at investigating all these aspects through the implementation of Work packages and tasks aimed at covering aspects related to modeling and algorithmic techniques, in theoretical grounding principles, in architectural and implementation issues, in policy and governance of technology, in legal and ethical principles of pervasive AI (Q1), in education and awareness and in human and artificial creative processes. In addition, a set of carefully selected pilot and use cases will experiment every aspect covered by work packages developing foundational research results.