Modal Logics of Higher-Order Probability
Peter Haddawy, Alan Frisch
This paper discusses the relationship between probability and modal logic. 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 O and 1 represents a range between impossibility and necessity, not between simple falsity and truth. We examine two classes of probability models: flat and staged. The flat models are straightforward generalizations of models for alethic logic. We show that one of the more interesting constraints relating higher- and lower-order probabilities forces all higher-order probabilities in flat models to be either zero or one. We introduce staged models as a means of avoiding this problem. Constraints on the two types of models define various classes of probability logics. We relate some of these probability logics to alethic logic.
PDF Link: /papers/88/p133-haddawy.pdf
AUTHOR = "Peter Haddawy
and Alan Frisch",
TITLE = "Modal Logics of Higher-Order Probability",
BOOKTITLE = "Uncertainty in Artificial Intelligence 4 Annual Conference on Uncertainty in Artificial Intelligence (UAI-88)",
PUBLISHER = "Elsevier Science",
ADDRESS = "Amsterdam, NL",
YEAR = "1988",
PAGES = "133--148"