There are many real-world problems where human expert skills in reasoning about complex systems are incomparably higher than the level of modern computing systems. At the same time there are even more areas where advances are required but human problem-so
lving skills can not be directly applied. For example, there are problems of planning and automatic control of autonomous agents such as space vehicles, stations and robots with cooperative and opposing interests functioning in a complex, hazardous enviro
nment. Reasoning about such complex systems should be done automatically, in a timely manner, and often in a real time. Moreover, there are no highly-skilled human experts in these fields ready to substitute for robots (on a virtual model) or transfer the
ir knowledge to them. There is no grand-master in robot control, although, of course, the knowledge of existing experts in this field should not be neglected Ð it is even more valuable. It is very important to study human expert reasoning about similar c
omplex systems in the areas where the results are successful, in order to discover the keys to success, and then apply and adopt these keys to the new, as yet, unsolved problems. Then, we meet a hard question. What language tools do we have for the adequa
te representation of human expert skills? An application of such language to the area of successful results achieved by the human expert should yield a formal, domain independent knowledge ready to be transferred to different areas. Neither natural nor pr
ogramming languages satisfy our goal. The first are informal and ambiguous, while the second are usually detailed, lower-level tools. Actually, we have to learn how we can formally represent, generate, and investigate a mathematical model based on the abs
tract images extracted from the expert vision of the problem.
There have been many attempts to find the optimal (suboptimal) operation for real-world complex systems. One of the basic ideas is to decrease the dimension of the real-world system following the approach of a human expert in a certain field, by breaking
the system into smaller subsystems. These ideas have been implemented for many problems with varying degrees of success. Implementations based on the formal theories of linear and nonlinear planning meet hard efficiency problems. An efficient planner requ
ires an intensive use of heuristic knowledge. On the other hand, a pure heuristic implementation is hardly reproduced for other problem domains. There is no general constructive approach to such implementations. Each new problem should be carefully studie
d and previous experience usually can not be applied. Basically, we can not answer the question: what are the formal properties of human heuristics which drove us to a successful hierarchy of subsystems for a given problem and how we can apply the same id
eas in a different problem domain.
In the 1960Õs a formal syntactic approach to the investigation of properties of natural language resulted in the fast development of a theory of formal languages by Chomsky, Ginsburg, and others. This development provided an interesting opportunity for di
ssemination of this approach to different areas. In particular, there came an idea of analogous linguistic representation of images. This idea was successfully developed into syntactic methods of pattern recognition by Fu, Narasimhan, and Pavlidis, and pi
cture description languages by Shaw, Feder, Phaltz and Rosenfeld.
Searching for the adequate mathematical tools formalizing human heuristics of dynamic hierarchy, we have transformed the idea of linguistic representation of complex real-world and artificial images into the idea of similar representation of complex hiera
rchical systems. However, the appropriate languages should possess more sophisticated attributes than languages usually used for pattern description. The origin of such languages can be traced back to the research on programmed attribute grammars by Knuth
, Rozenkrantz, and Volchenkov.
A mathematical environment (a ÒglueÓ) for the formal implementation of this approach was developed following the theories of formal problem solving and planning by Nilsson, Fikes, Sacerdoti, McCarthy, Hayes, and others based on first order predicate calcu
lus.
To show the power of the linguistic approach it is important that the chosen model of the heuristic hierarchical system be sufficiently complex, poorly formalized, and have successful applications in different areas. Such a model was developed by Botvinni
k, Stilman, and others, and successfully applied to scheduling, planning, control, and computer chess.
In order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, a formal theory, the Linguistic Geometry is being developed. This research includes the development of syntactic too
ls for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics, which allow the decomposition of complex systems into the hierarchy of subsystems, and thus solve intractabl
e problems reducing the search. These hierarchical images were extracted from the expert vision of the problem. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. The lowest level language, the Language of Trajectorie
s, is the formalization of the set of paths between the locations of elements of the system. Subsets of paths and elements unified in achieving (opposing) local goals form the next level languages, the Family of Trajectory Network Languages. The Language
of Zones, a member of this family, is applicable to military control systems. The highest level of the hierarchy of languages is the Family of Languages of Searches . It includes as members all the well known search algorithms, e.g., alpha-beta search, d
ynamic programming, etc. The Language of Translations, representing the search for the optimal operation in the hierarchy of subsystems, is a member of the same Family.