A Linguistic Approach to Geometric Reasoning

The objective of the research considered in this paper is to develop a theoretical foundation for the representation of large-scale hierarchical complex systems, so-called Linguistic Geometry. The research relies on the formalization of heuristics of high-skilled human experts which have resulted in the development of successful decision support systems. This approach is based on a broad application of the theory of formal languages and grammars as well as theories of formal problem-solving and planning on the basis of the first-order predicate calculus. This paper reports new results in the investigation of geometrical properties of the first-level subsystems (paths of elements) unified as Surface Linguistic Geometry. Theoretical constructions considered in this paper are illustrated employing comprehensive examples from power maintenance scheduling, robot control, chess game. A program implementation of this approach should generate decision support systems for a wide class of practical problems.