Open World Dempster-Shafer Using Complementary Sets

Dempster-Shafer Theory (DST) is a mathematical framework to handle imprecision and uncertainty in reasoning and decision making. One assumption of DST is that of a closed-world, or the assumption that all propositions are known a priori. In this work, we explore an alternative formulation of Dempster-Shafer that allows for the dynamic inclusion of new propositions. Specifically, we expand the framework to include the complement of every set of propositions. This adjustment enables an open-world interpretation that can support unspecified and dynamic propositions as we learn about the problem space. Including complementary sets distinguishes this from previous work in DST where the open world is attributed to the empty set. We demonstrate our open world Dempster-Shafer Theory on a variety of synthetic and real datasets.