Classical and Quantum Probabilities as Truth Values

Abstract

We show how probabilities can be treated as truth values in suitable sheaf topoi. The scheme developed in this paper is very general and applies to both classical and quantum physics. On the quantum side, the results are a natural extension of our existing work on a topos approach to quantum theory. Earlier results on the representation of arbitrary quantum states are complemented with a purely logical perspective.

39 pages, no figures

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Cited by in corpus (7)

• Understanding quantum mechanics: a review and synthesis in precise language
• The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations
• Topos Models for Physics and Topos Theory
• Conceptual and technical challenges of quantum gravity
• Topos quantum theory with short posets
• Topos Quantum Theory on Quantization-Induced Sheaves
• Topos Quantum Theory Reduced by Context-Selection Functors