Probability theory plays a central role in computer science, from causal inference to probabilistic programming and verification, machine learning, and probabilistic logic. Yet these areas often develop their mathematical foundations, terminology, and tools separately. Markov categories have emerged as a promising categorical framework for identifying the common structures underlying probabilistic reasoning. By abstracting away from model-specific measure-theoretic details while retaining the essential structure common to all those contexts, they offer both a high-level mathematical foundation and a graphical language, based on string diagrams, for reasoning about probability.

The main goal of this seminar is to bring together researchers working with a categorical angle on probability and statistics, focussing on causal inference and probabilistic programming and verification, and related areas. These communities increasingly use closely related categorical structures, but interactions between them remain fragmented. This Dagstuhl Seminar will seek to establish a common language, identify shared problems and potential solutions, and determine how developments in one application area can inform both the foundations and applications of Markov categories in others.

A first major topic will be the categorical reconstruction of classical probability and statistics. A growing number of fundamental results – including de Finetti-type theorems on random sequences and arrays, ergodic decomposition and Markov Chain Monte Carlo – have already been formulated and proved at the abstract level of Markov categories. The seminar will examine what categorical structure is required for such results and which major results remain to be understood categorically, with the central limit theorem providing an important open challenge. Closely related is the foundational question of whether probability admits a natural categorical axiomatization capable of explaining why familiar measure-theoretic models arise as canonical models of probabilistic computation.

A second focus will be causal reasoning and inference. String diagrams make dependencies and causal structure explicit and intuitive, providing a natural bridge between categorical semantics and traditional graphical formalisms like directed acyclic graphs. The seminar will investigate how graphical “diagram surgery” can support causal inference and probabilistic updating, including forms of inference beyond ordinary Bayesian conditioning, such as Jeffrey updating and expectation-maximisation techniques.

Third, the seminar will address the semantics of probabilistic programming. Combining higher-order computation, recursion, conditioning, and measure-theoretic probability remains technically difficult, and Markov categories offer a framework for isolating the structural requirements that suitable semantic models should satisfy. This connects to a broader goal of understanding which categorical structures characterize well-behaved notions of probabilistic computation.

By developing common notation and graphical conventions, comparing semantic frameworks and formulating a shared research agenda, the meeting will clarify the role that Markov categories can play as a unifying framework for probabilistic reasoning across mathematics and computer science and help bring together a currently fragmented research community.

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Elena Di Lavore, Tobias Fritz, Fabio Gadducci, and Bart Jacobs