Reasoning with uncertainty in deductive databases and logic program

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 thesis, we develop a few frameworks to rectify this situation. In the first part of our study, we introduce a deductive database language 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. Furthermore, we develop a proof procedure for this language, and present soundness and completeness results of this procedure.;As the aforementioned language is monotonic in nature, we discuss in the second half of this thesis three approaches of supporting non-monotonic probabilistic reasoning. In the first approach, we use a non-monotonic negation operator. We also present different semantical structures characterizing the semantics of such negations. All these structures are based on the stable semantics for classical logic programming. In the second approach, we use the Dempster-Shafer rule of combination. After developing a fixpoint theory for this approach, we present a precise relationship linking the Dempster-Shafer mode of non-monotonicity to the stable semantical approach introduced earlier.;So far, we have focussed entirely on using subjective probabilities. In the third approach, we discuss how empirical probabilities can be supported in monadic deductive databases. We first develop a model-theoretic characterization for such databases, and present a totally correct algorithm for checking consistency. Then we develop a sound and complete query answering procedure that supports non-monotonic reasoning based on changing reference classes.