In recent years, there has been a growing interest in reasoning with uncertainty in logic 
programming and deductive databases. However, most frameworks proposed thus far are either 
non-probabilistic in nature or based on subjective probabilities.  In this paper, we address 
the problem of incorporating empirical probabilities -- that is, probabilities obtained 
from statistical findings -- in deductive databases. To this end, we develop a formal 
model-theoretic basis for such databases. We also present a sound and complete algorithm 
for checking the consistency of such databases. Moreover, we develop consistency-preserving 
ways to optimize the algorithm for practical usage. Finally, we show how query answering 
for empirical deductive databases can be carried out.