QUALITATIVE PROBABILITIES FOR DEFAULT REASONING, BELIEF REVISION, ANDCAUSAL-MODELING

This paper presents a formalism that combines useful properties of bot h logic and probabilities, Like logic, the formalism admits qualitativ e sentences and provides symbolic machinery for deriving deductively c losed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in resp onse to changing observations. Rules are interpreted as order-of-magni tude approximations of conditional probabilities which impose constrai nts over the rankings of worlds. Inferences are supported by a unique priority ordering on rules which is syntactically derived from the kno wledge base. This ordering accounts for rule interactions, respects sp ecificity considerations and facilitates the construction of coherent states of beliefs, Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries, Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent be lief revision is embodied naturally and tractably. Finally, causal rul es are interpreted as imposing Markovian conditions that further const rain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal proj ections, explanations, actions and change.