Nicolae Tandareanu
Inheritance-Based Knowledge Systems And Their Answer Functions Computation Using Lattice Theory

Abstract.
The following aspects are developed in this paper. We give a formal description for an inheritance-based knowledge system and we define the corresponding answer function. The answer function for such a system is a recursive one and its values may be an attribute value, undefined or unknown.
The problem is to give an algorithm to compute the values of this function such that the values undefined and unknown are identified before the effective computation is realized. In order to obtain such an algorithm we use a kind of labelled tree and a distributive lattice of such trees, which are presented in detail in ([9], [10]). A necessary and sufficient condition for the existence of the greatest element in this lattice is also used ([9], [10]).
The algorithm CompK given in the last part of this paper uses this property to realize the proposed aim. We illustrate the application of this algorithm for a simple knowledge base in the last part of this paper.
Keywords: frame, inheritance, labelled tree, lattice, knowledge representation, knowledge base.