Some Preliminary Results on the Stableness of Extended F-rule Systems

In this paper we shall investigate an extended version of F-rule systems, in which each F-rule can include an arbitrary combination of disjunctions and conjunctions of atoms in the premise. The first main result here is a way to determine values assigned to these extended facts, based on two basic operators ⊕ and x;, which are shown to be equivalent to external probabilistic reasoning by resolving linear programming problem. Based on this, a definition on mixed inference operator for extended F-rule systems is discussed. We have shown that an extended F-rule system with the defined reasoning operator is stable iff its corresponding F-rule system is stable. This proposition allows us to apply all our available research results on F-rule systems to extended F-rule systems.