“Assigning Probabilities to Logical Formulas”, 1966 (; similar):
Probability concepts nowadays are presented in the standard framework of the Kolmogorov axioms. A sample space is given together with an σ-field of subsets, the events, and an σ-additive probability measure defined on this σ-field.
It is more natural in many situations to assign probabilities to statements rather than sets. It may be mathematically useful to translate everything into a set-theoretical formulation, but the step is not always necessary or even helpful. The main task is to carry over the standard concepts from ordinary logic to what might be called “probability logic.” Indeed ordinary logic is a special case: the assignment of truth values to formulas can be viewed as assigning probabilities that are either 0 (for false) or 1 (for true).
In a sense, the symmetric probability systems are opposite to ordinary relational systems.