Probabilistic and Quantum Event Structures

Ryusho Nemoto

Glynn Winskel

Building on a new definition and characterization of probabilistic event structures, a general definition of distributed probabilistic strategies is proposed. Probabilistic strategies are shown to compose, with probabilistic copy-cat strategies as identities. A higher-order probabilistic process language reminiscent of Milnerʼs CCS is interpretable within probabilistic strategies. W.r.t. a new definition of quantum event structure, it is shown how consistent parts of a quantum event structure are automatically probabilistic event structures, and so possess a probability measure. This gives a non-traditional take on the consistent-histories approach to quantum theory. It leads to an extension to quantum strategies. Probabilistic games extend to games with payoff, symmetry and games of imperfect information.

Dick J. Hoekzema

Elias Zafiris

Alexey A. Nekludoff

This paper argues that probabilistic structure should not be treated as ontologically primitive. Instead, probability is defined relative to conditions of recordability: it organizes spaces of possible records rather than properties of events as such. The analysis distinguishes between events, records, and probabilistic structures, and shows that probability acquires meaning only when stable, distinguishable, and reproducible records are available. In this view, Kolmogorovian probability theory provides a formally consistent framework, but does not specify how probabilistic domains arise from empirical observation. As a result, probabilistic formalism underdetermines ontology. Different ontological models can generate identical probabilistic structures, which implies that probability cannot serve as a direct guide to the nature of reality. The paper critically examines Ontic Structural Realism (OSR), arguing that it risks conflating representational structure with ontological structure. It concludes that any ontological interpretation of probabilistic or correlational structures requires independent justification beyond formalism.

Ph. Blanchard, Arkadiusz Jadczyk