Non-monotonic Negation in Probabilistic Deductive Databases
This work addresses a theoretical problem in AI and databases for researchers in logic programming and probabilistic reasoning, but appears incremental as it builds on existing stable semantics.
The paper tackles the problem of non-monotonic negation in probabilistic deductive databases by introducing stable formula functions and stable class semantics, demonstrating that these can handle default reasoning in probabilistic deduction.
In this paper we study the uses and the semantics of non-monotonic negation in probabilistic deductive data bases. Based on the stable semantics for classical logic programming, we introduce the notion of stable formula, functions. We show that stable formula, functions are minimal fixpoints of operators associated with probabilistic deductive databases with negation. Furthermore, since a. probabilistic deductive database may not necessarily have a stable formula function, we provide a stable class semantics for such databases. Finally, we demonstrate that the proposed semantics can handle default reasoning naturally in the context of probabilistic deduction.