We present a theoretical basis for supporting subjective and conditional probabilities in deductive databases. We design a language that allows a user greater expressive power than classical logic programming. In particular, a user can express the fact thatA is possible (i.e.A has non-zero probability),B is possible, but (A ⋀B) as a whole is impossible. A user can also freely specify probability annotations that may contain variables. The focus of this paper is to study the semantics of programs written in such a language in relation to probability theory. Our model theory which is founded on the classical one captures the uncertainty described in a probabilistic program at the level of Herbrand interpretations. Furthermore, we develop a fixpoint theory and a proof procedure for such programs and present soundness and completeness results. Finally we characterize the relationships between probability theory and the fixpoint, model, and proof theory of our programs.
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Ng, R., Subrahmanian, V.S. A semantical framework for supporting subjective and conditional probabilities in deductive databases. J Autom Reasoning 10, 191–235 (1993). https://doi.org/10.1007/BF00881836
- Subjective and conditional probabilities
- deductive databases
- probability theory