Context-Based Inferences from Probabilistic Conditionals with Default Negation at Maximum Entropy

The principle of maximum entropy (MaxEnt) constitutes a powerful formalism for nonmonotonic reasoning based on probabilistic conditionals. Conditionals are defeasible rules which allow one to express that certain subclasses of some broader concept behave exceptional. In the (common) probabilistic semantics of conditional statements, these exceptions are formalized only implicitly: The conditional (B|A)[p] expresses that if A holds, then B is typically true, namely with probability p, but without explicitly talking about the subclass of A for which B does not hold. There is no possibility to express within the conditional that a subclass C of A is excluded from the inference to B because one is unaware of the probability of B given C. In this paper, we apply the concept of default negation to probabilistic MaxEnt reasoning in order to formalize this kind of unawareness and propose a context-based inference formalism. We exemplify the usefulness of this inference relation, and show that it satisfies basic formal properties of probabilistic reasoning.