Systems of knowledge representation based on stratified graphs. Application in Natural Language Generation

The concept of stratified graph introduces some method of knowledge representation (see [Ţăndăreanu, N., Knowledge representation by labeled stratified graphs, Proc. 8th World Multi-Conference on Systemics, Cybernetics and Informatics, 5 (2004), 345–350; Ţăndăreanu, N., Proving the Existence of Labelled Stratified Graphs, An. Univ. Craiova Ser. Mat. Inform., 27 (2000), 81–92]) (\cite{ntand1}, \cite{ntand10}).
The inference process developed for this method uses the paths of the stratified graphs, an order between the elementary arcs of a path and some results of universal algebras. The order is defined by considering a structured path instead of a regular path.
In this paper we define the concept of system of knowledge representation as a tuple of the following components: a stratified graph , a partial algebra of real objects, an embedding mapping (an injective mapping that embeds the nodes of into objects of ) and a set of algorithms such that each of them can combine two objects of to get some other object of . We define also the concept of inference process performed by a system of knowledge processing in which the interpretation of the symbolic elements is defined by means of natural language constructions. In this manner we obtained a mechanism for texts generation in a natural language (for this approach, Romanian).