Topic Archive: probability space
Evidence aggregation is a well-known problem which appears naturally in many areas. A classical approach to this problem is via Bayesian probabilistic evidence aggregation. Our approach is radically different. We consider the following situation: suppose a proposition X logically follows from a database — a set of propositions D which are supported by some known evidence, vector u of events in a probability space. We answer the question of what is the best aggregated evidence for X justified by the given data. We show that such aggregated evidence e(u) could be assembled algorithmically from the collection of all logical derivations of X from D. This approach can handle conflicting and inconsistent data and allows the gathering both positive and negative evidence for the same proposition. The problem is formalized in a version of justification logic and the conclusions are supported by corresponding completeness theorems.