The logical consistency of a collection of assertions about events
can be viewed as a special case of coherent probability assessments
in the sense of de Finetti.
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References
[1] Buehler, R. J., "Coherent preferences", The Annals of Statistics, vol. 4 (1976), pp. 1051--64.
[2] de Finetti, B., "La prévision : ses lois logiques, ses sources subjectives", Annales de l'Institut Henri Poincaré, vol. 7 (1937), pp. 1--68. English translation in Studies in Subjective Probability, edited by H. Kyburg and H. Smokler, Krieger Publishing, Huntington, 1980.
[3] de Finetti, B., Probability, Induction and Statistics. The Art of Guessing, Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, New York, 1972.
[4] Enderton, H. B., A Mathematical Introduction to Logic, Academic Press, New York, 1972.
[5] Hailperin, T., Sentential Probability Logic. Origins, Development, Current Status, and Technical Applications, Associated University Presses, Cranbury, 1996.
[6] Heath, D., and W. Sudderth, "On finitely additive priors, coherence, and extended admissibility", The Annals of Statistics, vol. 6 (1978), pp. 333--45.
[7] Heath, D. C., and W. D. Sudderth, "On a theorem of de Finetti, oddsmaking, and game theory", Annals of Mathematical Statistics, vol. 43 (1972), pp. 2072--77.
[8] Joyce, J. M., "A nonpragmatic vindication of probabilism", Philosophy of Science, vol. 65 (1998), pp. 575--603.
[9] Lightstone, A. H., Mathematical Logic. An Introduction to Model Theory, edited by H. B. Enderton, vol. 9 of Mathematical Concepts and Methods in Science and Engineering, Plenum Press, New York, 1978.
Mathematical Reviews (MathSciNet):
MR497355
[10] Skyrms, B., Pragmatics and Empiricism, Yale University Press, New Haven, 1984.