Using equivalences of worlds for aggregation semantics of relational conditionals

Abstract

For relational probabilistic conditionals, the so-called aggregation semantics has been proposed recently. Applying the maximum entropy principle for reasoning under aggregation semantics requires solving a complex optimization problem. Here, we improve an approach to solving this optimization problem by Generalized Iterative Scaling (GIS). After showing how the method of Lagrange multipliers can also be used for aggregation semantics, we exploit that possible worlds are structurally equivalent with respect to a knowledge base if they have the same verification and falsification properties. We present a GIS algorithm operating on the induced equivalence classes of worlds; its implementation yields significant performance improvements. © 2012 Springer-Verlag.