The Probability of a Possibility: Adding Uncertainty to Default Rules
This work addresses foundational issues in AI and logic for researchers in knowledge representation, offering a novel integration of qualitative and probabilistic methods, though it appears incremental in combining existing theories.
The paper tackles the problem of integrating uncertainty into default reasoning and belief revision by developing a semantics that treats conditional sentences as statements of conditional probability, enabling meaningful revision even with zero-probability sentences through counterfactual probabilities. It unifies probability and possibility theory, showing connections to Lewis's imaging method.
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A were believed, then B would be believed to degree p." This method of revision extends conditionalization by allowing meaningful revision by sentences whose probability is zero. This is achieved through the use of counterfactual probabilities. Thus, our system accounts for the best properties of qualitative methods of update (in particular, the AGM theory of revision) and probabilistic methods. We also show how our system can be viewed as a unification of probability theory and possibility theory, highlighting their orthogonality and providing a means for expressing the probability of a possibility. We also demonstrate the connection to Lewis's method of imaging.