In this paper we shall propose a knowledge representation method, the deduction process in a knowledge representation and reasoning system using this method and therefore the answer function of such a system. This is an algebraic method because some concepts of universal algebra are used. More precisely, we introduce the concept of knowledge base with output (KBO), the central structure being that of labeled stratified graph. For such a base we distinguish a structure and two kinds of computations. The structure is described by a labeled stratified graph and an output space. The computations in a KBO are represented by two levels: syntactic and semantic. Both the syntactic and the semantic computations in a KBO are described in this paper. Finally, we exemplify all the concepts and we apply the method to solve a given problem in travel scheduling. All the theoretical results are proved in a separate section.