Of all scientific investigations into reasoning with uncertainty and chance, probability 
theory is perhaps the best understood paradigm. Nevertheless, all studies conducted thus 
far on the semantics of quantitative logic programming have been restricted to 
non-probabilistic semantical characterizations.  In this paper, we survey the major 
features and summarize the major results of the various frameworks that we have developed 
to rectify this situation. In the first part of this paper, we outline a deductive database 
framework which is expressive enough to represent such probabilistic relationships as 
conditional probabilities, Bayesian updates, probability propagation and mutual exclusion.
We propose a fixpoint theory and a probabilistic model theory, and characterize their 
inter-relationships.  As the aforementioned language is monotonic in nature, we discuss in 
the second half of this paper three approaches of supporting non-monotonic probabilistic 
reasoning. In the first approach, we use a non-monotonic negation operator. In the second, 
we use the Dempster-Shafer rule of combination. Finally, we discuss how empirical 
probabilities can be supported in monadic deductive databases.