# Justification Logic and Aggregating Probabilistic Evidence

## Sergei Artemov

### The CUNY Graduate Center

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.

Professor Artemov holds a Distinguished Professor position at the Graduate Center of the City University of New York, in the Computer Science, Mathematics and Philosophy programs. He is also Professor of Mathematics at Moscow State University, the founder and the Head of the research laboratory Logical Problems in Computer Science. He conducts research in the areas of logic in computer science, mathematical logic and proof theory, knowledge representation and artificial intelligence, automated deduction and verification and optimal control and hybrid systems.