## Abstract

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 that*A* 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

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### Key words

- Subjective and conditional probabilities
- deductive databases
- probability theory