Probability as a Modal Operator
This work addresses foundational issues in AI and logic by reinterpreting probability as a modal continuum between impossibility and necessity, offering a novel framework for reasoning.
The paper argues for viewing probability as a modal operator, presenting a logic with clear semantics for quantification and higher-order probabilities, and shows it is natural and useful for expressing probabilistic and logical concepts.
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.