Factorization of an inheritance knowledge base (I)
In  we introduced a model of an extended inheritance for knowledge representation. This model allows the multiple inheritance and includes a parameter for each attribute value. This parameter can describe some features of the attribute values, for example the uncertainty. This paper is a starting point for a possible research line to study the decomposition of these knowledge bases into disjoint components. This is named the factorization problem. The name comes from the fact that the set of all components of a knowledge base K is the factor set Obj(K)/ρ~K, where Obj(K) is the set of all objects of K and ρ~Kis an equivalence relation defined by means of the inheritance from K. A necessary and sufficient condition for factorization is given. All the results proved in this paper and in  constitute the algebraic background of a forthcoming paper as we mention in the last section.