Hierarchical Distributed Reasoning System for Geometric Image Generation
The concept of hierarchical reasoning system was introduced in [5], where gut intuitive method to build such systems based on their inputs is given. In thus paper we formalize several concepts which open a possible research line concerning the use of these structures. A hierarchical reasoning system H is a directed graph organized on several levels such that each node of the level j is a hyper-schema of order j. As a mathematical structure, H is an abstract one and a special kind of formal computation is introduced. As a result of this computation we obtain a set F(H) of formulas. We explain what we understand by an interpretation of H and define its corresponding semantical computation. By means of an interpretation J(H) for H and applying the rules of the semantical computation, each element of w is an element of F(H) becomes some object J(w) of a given space. We exemplify these concepts and we show that for two distinct interpretations J(1) (H) and J(2)(H) for the same system H, a given formula w is an element of F(H) is transformed into a sentence J(1) (w) of a natural language whereas J(2)(w) is a geometric image. A short description of a Java implementation of a hierarchical system generating images is also given in a separate section. By examples we show that the mechanism introduced in this paper allows us to model the distributed knowledge. Finally several open problems are specified.
distributed reasoning system geometrical image generation hyper-schema interpretation semantic schema