Linguistic Geometry: The Age of Maturity
Boris Stilman*,**, Vladimir Yakhnis*, and Oleg Umanskiy*,**
*STILMAN Advanced Strategies, 1623 Blake Street, Suite 200, Denver, CO 80202, USA
**Department of Computer Science, University of Colorado Denver, Campus Box 109, Denver, CO 80217-3364, USA
This paper describes the current status of research and applications of Linguistic Geometry (LG), a type of game theory scalable to the level of real life defense systems. LG is compared to conventional gaming approaches with respect to their applicability to real world problems. LG generates winning strategies for all sides in a conflict in real time by constructing them out of a limited set of blocks called zones. Several examples of zones are introduced. The paper describes the process of discovery of new zones essential for various types of military operations, which represent different classes of abstract board games. We also included a brief explanation of scalability of the LG applications. This paper describes a universal tool kit, LG-PACKAGE, which allows a user to build his/her own applications of LG. This tool kit includes GDK (Game Development Kit), GIK (Game Integration Kit), GRT (Game Resource Tool), GST (Game Solving Tool), GNS (Game Network Services) and GMI (Game Mobile Interface). In the end we included a description of the most advanced experiments with the LG applications conducted by DARPA and US Army and assessments of these experiments by military experts.
-  G. D. Brewer and M. Shubik, “The War Game: A Critique of Military Problem Solving,” Harvard University Press, 1979.
-  J. Dunnigan, “The Complete Wargames Handbook,” William Morrow & Co., 1992.
-  J. D. Williams, “The Complete Strategist,” Dover Publications, 1986.
-  “Linguistic Geometry Tools: LG-PACKAGE,” with 8 movies on Demo DVD, p. 60, STILMAN, 2009. This brochure and recorded movies are available at
-  R. M. Jones, J. E. Laird, P. E. Nielsen, K. J. Coulter, P. Kenny, and F. V. Koss, “Automated Intelligent Pilots for Combat Flight Simulation,” AI Magazine, Spring 1999.
-  D. Pugh, Captain, USAF, “A Validation Assessment of the STORM Air-to-Air Prototype Algorithm,” AFIT.
-  D. Knuth and R. Moore, “An Analysis of Alpha-Beta Pruning,” Artificial Intelligence, Vol.6, No.4, pp. 293-326, 1975.
-  B. Stilman, “Linguistic Geometry: From Search to Construction,” Kluwer Acad. Publishers (now Springer-Verlag), p. 416, 2000.
-  B. Stilman, V. Yakhnis, and O.Umanskiy, “Knowledge Acquisition and Strategy Generation with LG Wargaming Tools,” Int. J. of Comp. Intelligence and Appl., Vol.2, No.4, pp. 385-410, 2002.
-  M. M. Botvinnik, “Computers in Chess: Solving Inexact Search Problems,” Springer-Verlag, 1984.
-  DARPA RAID program, IPTO (Information Processing Technology Office), 2004-08,
-  B. Stilman, V. Yakhnis, and O. Umanskiy, Chapter 3.3. Strategies in Large Scale Problems, in: “Adversarial Reasoning: Computational Approaches to Reading the Opponent’s Mind,” Ed. by A. Kott and W. McEneaney, Chapman & Hall/CRC, pp. 251-285, 2007.
-  M. Osborn and A. Rubinstein, “A Course in Game Theory,” MIT Press, Cambridge, MA, 1994.
-  R. Isaacs, “Differential Games,” Wiley, New York, NY, 1965.
-  H. W. Kuhn, Tucker, A. W., eds. “Contributions to the Theory of Games,” Volume II (Annals of Mathematics Studies, 28), Princeton University Press, 1953.
-  J. Von Neumann and O. Morgenstern, “Theory of Games and Economic Behavior,” Princeton Univ. Press, 1944.
-  A. Garcia-Ortiz et al., “Application of Semantic Control to a Class of Pursue-Evader Problems,” Computers and Mathematics with Applications, Vol.26, No.5, pp. 97-124, 1993.
-  Y. Lirov, E. Y. Rodin, B. G. McElhaney, and L. W. Wilbur, “Artificial Intelligence Modeling of Control Systems,” Simulation, Vol.50, No.1, pp. 12-24, 1988.
-  B. Stilman, V. Yakhnis, O. Umanskiy, and J. Hearing, “Operational Level Decision Aids with LG-based Tools,” Proc. of the SPIE Conf. “Enabling Technology for Simulation Science VI”, pp. 403-414, Orlando, FL, USA, April 1-5, 2002.
-  “Linguistic Geometry Workshop, with STILMAN’s Comments,” p. 17, REPORT, Dstl, Ministry of Defence, Farnborough, UK, Feb., pp. 25-26, 2003.
-  GIK Designer Guide, p. 27, STILMAN Advanced Strategies, 2009.
-  Jane’s International Defence Review, “Interview: Dr Alexander Kott, RAID Programme Manager,” March 2008.
-  A. Kott, “Raiding The Enemy’s Mind,” Military Information Technology, Online Edition, Dec 29, 2007.
-  B. Stilman, “Linguistic Geometry for Symmetric and Asymmetric War Games,” Proc. of the 2nd Int. Conf. on Computers and Games – CG’2000, pp. 431-449, Hamamatsu, Japan, Oct. 26-28, 2000.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.