Boris Stilman

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.

Network Languages for Complex Systems

Abstract In this paper, we describe research on two-dimensional geometrical structures for complex systems to accomplish applications to robotics, process planning and control, scheduling, decision support, etc. This research includes the development of tools for representation and reasoning about hierarchical networks of paths that are inherent for complex real-world systems. It relies on the formalization of search heuristics of high-skilled human experts which have resulted in the development of successful applications in different areas. The proposed 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 employing the first-order predicate calculus. A performance of implementations is considered in detail.

Translations of network languages

Abstract In this paper, we describe new results of research on geometrical properties of complex control systems, the so-called Linguistic Geometry. This research includes the development of syntactic tools for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics of high-skilled human experts that have resulted in the development of successful applications in different areas. A hierarchy of subsystems of a complex system, the networks of paths, is represented as a hierarchy of formal languages. In this paper, we investigate transformations of these networks while a system moves from one state to another. The investigation consists of formal, constructive separation of changed and unchanged parts of system representation, the hierarchy of languages. Thus, we address a problem relative to the well-known Frame Problem for planning systems. A partial solution is presented in the form of the theorem about translations of network languages. Formal considerations are illustrated by example of Air Force robotic vehicles.

The Primary Language of ancient battles

Linguistic Geometry (LG) is a type of game theory for extensive discrete games scalable to the level of real life defense systems. This scalability is based on changing the paradigm for game solving: from search to construction. LG was developed by generalizing experiences of the advanced chess players. In this paper we embolden further a hypothesis that LG is an objective reality that existed long before the invention of the game of chess. We suggest that LG is a formal model of human thinking about armed conflict, a mental reality that existed for thousands of years. LG is a special purpose network-based language, a warfighting component of the Primary Language of the human brain. (Existence of the Primary Language was suggested by J. von Neumann in 1957.) Moreover, the origin of the warfighting component could be traced back for hundreds of thousands of years to the origin of human species. We suggest that the development of this model of the human brain was stimulated by constant hunting and fighting. In this paper we also discuss striking similarities and differences of the LG language and another biological coding system, the genetic code. A major part of this paper is devoted to the detailed LG-based analysis of the three battles of Hannibal demonstrating that the LG-based software will generate the same resource allocation, deception and courses of action as those reported by the historians. It appears that by the time of Hannibal, the LG component and, probably, the entire Primary Language, had already been developed to full capacity.

Winning strategies for robotic wars: defense applications of linguistic geometry

This paper reports new results of research, which started in 1972 in Moscow, USSR. For 16 years Boris Stilman was involved in the advanced research project PIONEER led by a formed World Chess champion, Professor Mikhail Botvinnik. The goal of the project was, at first, to discover and mathematically formalize methodologies utilized by the most advanced chess experts (including Botvinnik himself) in solving chess problems almost without search. The next step was to apply this new theory to complex search problems from various problem domains. In the 1980s, in Moscow, Stilman developed the foundations of the new approach. In 1991, while at McGill University, Montreal, Canada, Stilman coined the term “Linguistic Geometry” (LG) as a name for the new theory for solving Abstract Board Games. After 1991, this research continued at the University of Colorado at Denver, USA. In 1995, V. Yakhnis joined the LG effort. In the 1990s, it was shown that LG is applicable to a wide class of higher-dimensional, multi-agent games with concurrently moving agents, which are ideally suited for combat planning and control. Also, it was proved that for several classes of games LG generates optimal strategies in polynomial time. This groundbreaking results also suggests that for much wider classes of games LG strategies are also optimal or close to optimal. Over a hundred papers on LG have been published. Stilman wrote the first scholarly book on LG,Linguistic Geometry: From Search to Construction, published in February 2000. Over the last two years, defense applications of LG have attracted so much attention at the Defense Advanced Research Projects Agency (DARPA), Rockwell, and Boeing that the number of LG-based projects has skyrocketed. In 1999, recognizing the maturity and power of this technology, a group of scientists, engineers, and entrepreneurs founded a company, STILMAN Advanced Strategies, to facilitate development of government and commercial applications of LG.

Managing search complexity in linguistic geometry

This paper is a new step in the development of linguistic geometry. This formal theory is intended to discover and generalize the inner properties of human expert heuristics, which have been successful in a certain class of complex control systems, and apply them to different systems. In this paper, we investigate heuristics extracted in the form of hierarchical networks of planning paths of autonomous agents. Employing linguistic geometry tools the dynamic hierarchy of networks is represented as a hierarchy of formal attribute languages. The main ideas of this methodology are shown in the paper on two pilot examples of the solution of complex optimization problems. The first example is a problem of strategic planning for the air combat, in which concurrent actions of four vehicles are simulated as serial interleaving moves. The second example is a problem of strategic planning for the space comb of eight autonomous vehicles (with interleaving moves) that requires generation of the search tree of the depth 25 with the branching factor 30. This is beyond the capabilities of modern and conceivable future computers (employing conventional approaches). In both examples the linguistic geometry tools showed deep and highly selective searches in comparison with conventional search algorithms. For the first example a sketch of the proof of optimality of the solution is considered.

Network languages for concurrent multiagent systems

Abstract This paper reports new results in the development of Linguistic Geometry towards concurrent multiagent aerospace systems. This formal theory is intended to discover the inner properties of human expert heuristics, which have been successful in a certain class of complex control systems, and apply them to different systems. The Linguistic Geometry relies on the formalization of search heuristics of the highly-skilled human experts, which allow for the decomposition of a complex system into a dynamic hierarchy of subsystems, and thus solve intractable problems by reducing the search dramatically. In this paper, we consider briefly the Linguistic Geometry tools and their application to multiagent systems represented 2D optimization problems for autonomous robotic vehicles in aerospace environment. First, we consider only serial motions, then we relax these constraints by allowing the cooperating agents move simultaneously if necessary while the motions of opposing agents alternate. Next we relax these constraints completely by allowing all the agents move simultaneously if necessary. A comparison of the searches for serial and concurrent cases shows that search reduction achieved in all types of problems with concurrent motions is even more dramatic than it was in the serial one.

Syntactic Hierarchy for Robotic Systems

This article reports new results of research on techniques for the search for the optimal suboptimal operation of complex control systems, especially robotic systems. To discover the inner, domain-independent properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, so-called linguistic geometry. This research includes the development of syntactic tools for knowledge representation and reasoning about large-scale hierarchical complex systems. It relies on the formalization of search heuristics of high-skilled human experts, which allow to decompose a complex system into a hierarchy of subsystems and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This article includes an informal survey of linguistic geometry, major formal issues, and detailed consideration of linguistic geometry of robotic autonomous vehicles.

Discovering the discovery of the hierarchy of formal languages

The hierarchy of formal languages is a mathematical representation of linguistic geometry (LG). LG is a type of game theory for a class of extensive discrete games called abstract board games (ABG), scalable to the level of real life defense systems. LG is a formal model of human reasoning about armed conflict, a mental reality “hard-wired” in the human brain. LG, an evolutionary product of millions of years of human warfare, must be a component of the primary language of the human brain (as introduced by Von Neumann). Experiences of development of LG must be instructive for solving another major puzzle, discovering the algorithm of discovery, yet another ancient component of the primary language. This paper reports results on discovering mental processes involved in the development of the hierarchy of formal languages. Those mental processes manifesting execution of the algorithm of discovery are called visual streams. This paper reveals the visual streams that were involved in the thought experiments led to the development of the formal theory of LG. Specifically, it demonstrates the streams involved in choosing the formal-linguistic representation of LG; the type of formal languages and grammars, the so-called controlled grammars; the construction of the grammars of shortest trajectories and the grammar of zones. This paper introduces a hypothesis of how we construct and focus visual streams.

Discovering the discovery of Linguistic Geometry

Linguistic Geometry (LG) is a type of game theory for extensive discrete games scalable to the level of real life defense systems. This scalability is based on changing the paradigm for game solving—from search to construction. LG was developed by generalizing experiences of the advanced chess players. LG is a formal model of human reasoning about armed conflict, a mental reality “hard-wired” in the human brain. It appears that this algorithm, an evolutionary product of millions of years of human warfare, served in its turn as the principle mover for evolution of human intelligence. Its special role in human history and its relationship to the Primary Language of the human brain (as introduced by J. Von Neumann) suggest that the experiences of development of LG must be instructive for solving another major puzzle, discovering the Algorithm of Discovery. This algorithm should be an ancient component of the Primary Language as well. This paper refining our experiences of discovering LG reports the first results of this research.