# Hierarchical Distributed Reasoning System for Geometric Image Generation

## Keywords:

semantic schema, interpretation, hyper-schema, distributed reasoning system, geometrical image generation## Abstract

The concept of hierarchical reasoning system was introduced in [5], where an intuitive method to build such systems based on their inputs is given. In this 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 I(H) for H and applying the rules of the semantical computation, each element of w in F(H) becomes some object I(w) of a given space. We exemplify these concepts and we show that for two distinct interpretations I1(H) and I2(H) for the same system H, a given formula w in F(H) is transformed into a sentence I1(w) of a natural language whereas I2(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.## References

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