Probability as a Modal Operator
Alan Frisch, Peter Haddawy
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a continuum between impossibility and necessity, not between simple falsity and truth. The present work provides a clear semantics for quantification into the scope of the probability operator and for higher-order probabilities. Probability logic is a language for expressing both probabilistic and logical concepts.
PDF Link: /papers/88/p109-frisch.pdf
AUTHOR = "Alan Frisch
and Peter Haddawy",
TITLE = "Probability as a Modal Operator",
BOOKTITLE = "Proceedings of the Fourth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-88)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "1988",
PAGES = "109--118"