Conditionals, Information, and Inference

Conditionals are fascinating and versatile objects of knowledge representation. On the one hand, they may express rules in a very general sense, representing, for example, plausible relationships, physical laws, and social norms. On the other hand, as default rules or general implications, they constitute a basic tool for reasoning, even in the presence of uncertainty. In this sense, conditionals are intimately connected both to information and inference. Due to their non-Boolean nature, however, conditionals are not easily dealt with. They are not simply true or false - rather, a conditional "if A then B" provides a context, A, for B to be plausible (or true) and must not be confused with "A entails B" or with the material implication "not A or B." This ill- trates how conditionals represent information, understood in its strict sense as reduction of uncertainty. To learn that, in the context A, the proposition B is plausible, may reduce uncertainty about B and hence is information. The ab- ity to predict such conditioned propositions is knowledge and as such (earlier) acquired information. The ?rst work on conditional objects dates back to Boole in the 19th c- tury, and the interest in conditionals was revived in the second half of the 20th century, when the emerging Arti?cial Intelligence made claims for appropriate formaltoolstohandle"generalizedrules."Sincethen,conditionalshavebeenthe topic of countless publications, each emphasizing their relevance for knowledge representation, plausible reasoning, nonmonotonic inference, and belief revision.

Invited Papers.- What Is at Stake in the Controversy over Conditionals.- Reflections on Logic and Probability in the Context of Conditionals.- Acceptance, Conditionals, and Belief Revision.- Regular Papers.- Getting the Point of Conditionals: An Argumentative Approach to the Psychological Interpretation of Conditional Premises.- Projective Default Epistemology.- On the Logic of Iterated Non-prioritised Revision.- Assertions, Conditionals, and Defaults.- A Maple Package for Conditional Event Algebras.- Conditional Independences in Gaussian Vectors and Rings of Polynomials.- Looking at Probabilistic Conditionals from an Institutional Point of View.- There Is a Reason for Everything (Probably): On the Application of Maxent to Induction.- Completing Incomplete Bayesian Networks.