This PhD project at The University of Manchester focuses on developing formally verified neuro-symbolic AI for robotics, targeting autonomous systems in hazardous environments such as nuclear decommissioning and space exploration. The project addresses the need for a fundamental shift in how autonomous robotic systems are specified, verified, and assessed, particularly as they increasingly rely on advanced forms of artificial intelligence. The research explores the integration of symbolic AI (knowledge-driven, rule-based systems) and sub-symbolic AI (data-driven, neural networks and machine learning) into neuro-symbolic (NeSy) AI paradigms, aiming to combine the transparency and verifiability of symbolic AI with the flexibility and efficiency of sub-symbolic AI. The methodology involves identifying relevant combinations of symbolic and sub-symbolic AI for critical autonomous robotic systems, systematically analyzing and formally specifying their requirements, and transforming these into reusable neuro-symbolic reasoning specification patterns. These patterns will be encoded as templates in the Formal Requirements Elicitation Tool (FRET), potentially extending the tool, and domain-specific contracts will be derived and verified using appropriate formal methods. The project will develop taxonomies of NeSy designs, analyze trade-offs (such as safety versus efficiency and interpretability versus speed), and design verification strategies for each specification pattern. Prototype tool support will be developed, leveraging FRET as a base. Expected outcomes include a catalogue of NeSy AI combinations in robotics, a set of reusable specification patterns, tool-supported verification strategies, and a collection of verified NeSy AI robotic components. The project offers opportunities for high-quality publications and collaboration with leading organizations such as NASA, Airbus, and others, supporting networking, internships, and career development. Applicants should have at least a 2.1 honours degree or a master’s in a relevant science or engineering discipline. The position is fully funded for 3.5 years for excellent candidates, with additional scholarships and studentships available. The start date is October 2026, and the application deadline is 13th March 2026. The University of Manchester is committed to equality, diversity, and inclusion, and encourages applications from all backgrounds. Flexible study arrangements may be considered. For more information and to apply, visit the university's application portal.