### Factorization of an inheritance knowledge base (I)

#### Abstract

In [4] 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^{~}*, where*_{K}*Obj*(*K*) is the set of all objects of*K*and ρ^{~}*is an equivalence relation defined by means of the inheritance from*_{K}*K*. A necessary and sufficient condition for factorization is given. All the results proved in this paper and in [5] constitute the algebraic background of a forthcoming paper as we mention in the last section.