Concetta Press

@article{robson2026QDNT,
  title={From Leibniz' Quest to Dirac Notation: Toward a Digital Epistemology for Reasoning under Uncertainty in Patient-Centric Learning Healthcare Systems},
  author={Rebhan, M, Ferrarello, L, Freidank, M, Moniatte, M, Ranatunge, R, Seebode, C, & Robson, B},
  journal={Journal of Biomedical Informatics and AI},
  volume={1},
  number={1},
  pages={5},
  year={2026},
  doi={10.5281/zenodo.20719208},
  publisher={Concetta Press},
  url={https://concettapress.net/article_From_Leibniz'_Quest_to_Dirac_Notation.html},
  pdf={https://concettapress.net/pdf/JBIAI_1_1_5(2026).pdf}
}

Abstract. At the dawn of the scientific age, before scientific disciplines had clearly marked boundaries, Leibniz was a polymath on the quest for a language that would enable reasoned discourse to be resolved by calculation (or formal inference), using mathematically precise notation, across different intellectual traditions. Today, enabled by scientific progress, there is interplay between human and machine intelligence, new ways of encoding certain and uncertain knowledge, and new ways of organizing work based on knowledge. We propose a contemporary interpretation of Leibniz’ vision as a ‘digital epistemology’ for AI in medicine, focusing on difficult medical cases where evidence-based decision making by patients and healthcare professionals is non-trivial. In this approach, reasoning is based on Dirac notation and algebra based on hyperbolic-complex (split-complex) vector spaces as a mathematical foundation. Dirac’s system has served science for almost a century, and as Dirac noted, it should be applicable to all aspects of human thought where numbers such as probabilities are involved (Dirac, 1930). To allow such learning systems to discover and validate the most informative patterns in patient data, combining human and machine intelligence, Open-Science-style transparency is used, rather than ‘black box AI’, including its encoding of uncertainty, contradictions, and conflicting recommendations. With increasing “FAIRification” (i.e. the process of making health-related data Findable, Accessible, Interoperable, and Reusable), and new health data spaces (federations across health data silos), we propose that we should soon have improved frame conditions for building such learning systems using the proposed digital epistemology. By “learning system” is usually meant a system that seeks to minimize the disagreement between the predictions the system makes and the actual situations; the minimization may involve local minima. However, any system that extracts knowledge, such as data analytics and data mining, can be considered as learning from data. We discuss systems designed for the translation of P4 science, i.e. systems that aim to make care more Personalized, Preventive, Participatory and Predictive, digital twins, and the modeling and simulation of patient trajectories, including trajectories that do not map well to the medical knowledge and evidence landscape. We refer to these as unguided patients, who typically have little recorded data. Importantly, however, they are patients who are clearly different from the populations studied in large clinical studies.

Keywords: healthcare; Leibniz; universal exchange language; unguided patients