Non-monotonic Negation in Probabilistic Deductive Databases

TL;DR

This paper explores the semantics of non-monotonic negation in probabilistic deductive databases, introducing stable formula functions and a stable class semantics to handle default reasoning.

Contribution

It introduces the concept of stable formula functions and a stable class semantics for probabilistic deductive databases with negation, extending classical logic programming semantics.

Findings

Stable formula functions are minimal fixpoints of associated operators.

A stable class semantics can be applied when stable formula functions do not exist.

The semantics naturally support default reasoning in probabilistic deduction.

Abstract

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.