Abstract
A formal theory introduced in this paper, the Linguistic Geometry, includes mathematical tools for knowledge representation and reasoning about multiagent discrete pursuit-evasion games. These class of games is an adequate mathematical model for the real world combat operations, particularly, for the aerospace and navy problem domains. Linguistic Geometry relies on the formalization of search heuristics, which allow one to decompose the game into a hierarchy of images (subsystems), and thus solve otherwise intractable problems by reducing the search dramatically. These hierarchical images extracted in the form of networks of paths from the expert vision of the problem are formalized as a hierarchy of formal languages. An example of the game is considered. While the solution of this problem was presented in other publications this is the first paper when we prove optimality of the solution. We conclude that for a certain class of search problems Linguistic Geometry tools, a set of heuristic algorithms, generate optimal solutions.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Botvinnik, M.M. (1984). Computers in Chess: Solving Inexact Search Problems. Springer Series in Symbolic Computation, New York: Springer-Verlag.
Botvinnik, M., Petriyev, E., Reznitskiy, A., et al. (1983). Application of New Method for Solving Search Problems For Power Equipment Maintenance Scheduling. Economics and Mathematical Methods (1030–1041), 6, (in Russian).
Chomsky, N. (1963). Formal Properties of Grammars. in Handbook of Mathematical Psychology, eds. R.Luce, R.Bush, E. Galanter., vol. 2 (323–418). New York: Wiley.
Feder, J. (1971). Plex languages. Inform. Sciences, 3,(225–241).
Fikes, R.E. and Nilsson, N.J. (1971). STRIPS: A New Approach to the Application of Theorem Proving in Problem Solving. Artificial Intelligence 2 (189–208).
Fu, K.S. (1982). Syntactic Pattern Recognition and Applications, Prentice Hall, Englewood Cliffs.
Ginsburg, S. (1966). The Mathematical Theory of Context-Free Languages, McGraw Hill, New York.
Knuth, D.E. (1968). Semantics of Context-Free Languages. Mathematical Systems Theory, (127–146), 2.
McCarthy, J. (1980). Circumscription-A Form of Non-Monotonic Reasoning. Artificial Intelligence, (27–39), 13.
McCarthy, J. and Hayes, P.J. (1969). Some Philosophical Problems from the Standpoint of Artificial Intelligence. Machine Intelligence (463–502), 4.
Narasimhan, R.N. (1966). Syntax-Directed Interpretation of Classes of Pictures. Comm. of ACM (166–173), 9.
Nilsson, N.J. (1980). Principles of Artificial Intelligence, Palo Alto, CA: Tioga Publ.
Pavlidis, T. (1977). Structural Pattern Recognition, New York: Springer-Verlag.
Rosenfeld, A. (1979). Picture Languages, Formal Models for Picture Recognition, Academic Press.
Rozenkrantz, D.J. (1969). Programmed Grammars and Classes of Formal Languages, J. of ACM (107–131), 1.
Sacerdoti, E.D. (1975). The Nonlinear Nature of Plans, Proc. Int. Joint Conference on Artificial Intelligence.
Shaw, A.C. (1969). A Formal Picture Description Scheme as a Basis for Picture Processing System, Information and Control (9–52), 19.
Shinar, J., (1990). Analysis of Dynamic Conflicts by Techniques of Art. Intelligence, INRIA Report, Antipolis.
Stilman, B. (1977). The Computer Learns. in Levy, D., 1976 US Computer Chess Championship (83–90). Computer Science Press, Woodland Hills, CA.
Stilman, B. (1985). Hierarchy of Formal Grammars for Solving Search Problems. In Artificial Intelligence. Results and Prospects, Proc. of the Int. Workshop (63–72), Moscow, (in Russian).
Stilman, B. (1993a). A Linguistic Approach to Geometric Reasoning, Int. J. Computers and Mathematics with Applications (29–57), 26(7).
Stilman, B. (1993b). Network Languages for Complex Systems, Int. J. Computers and Mathematics with Applications (51–79), 26(8).
Stilman, B. (1993c). Syntactic Hierarchy for Robotic Systems, Integrated Computer-Aided Engineering(57–81), 1(1).
Stilman, B. (1993d). A Formal Language for Hierarchical Systems Control, Languages of Design (333–356), 1(4).
Stilman, B. (1994a). Translations of Network Languages. Int. J. Computers and Mathematics with Applications (65–98), 27(2).
Stilman, B. (1994b). A Formal Model for Heuristic Search. Proc. of the 22nd Annual ACM Computer Science Conf., (380–389), March 8–10, Phoenix, AZ.
Stilman, B. (1994c). Heuristic Networks for Space Exploration, Telematics and Informatics, Int. J. on Telecommunication & Information Technology, 11(4), (403–428).
Stilman, B., (1994d) A Linguistic Geometry for Control Systems Design, Int. J. of Computers and Their Applications, (89–110), Vol. 1, No. 2, Dec. 1994.
Stilman, B., (1995a) Deep Search in Linguistic Geometry, SYMPOSIUM ON LINGUISTIC GEOMETRY AND SEMANTIC CONTROL, Proc. of the First World Congress on Intelligent Manufacturing: Processes and Systems, (868–879), Mayaguez, Puerto Rico, Feb. 1995.
Stilman, B., (1995b) A Linguistic Geometry for 3D Strategic Planning, Proc. of the 1995 Goddard Conference on Space Applications of Artificial Intelligence and Emerging Information Technologies, (279–295), NASA Goddard Space Flight Center, Greenbelt, MD, USA, May 1995.
Stilman, B., (1995c) A Linguistic Geometry for Multiagent Systems, Proc. of The 8th International Conference on Industrial & Engineering Applications of Artificial Intelligence & Expert Systems-IEA/AIE, (3–12), Melbourne, Australia, June 1995.
Stilman, B., (1995d) Total Concurrency and Uncertainty in Linguistic Geometry, Proc. of the IEEE International Symposium on Intelligent Control, (79–84), Monterey, CA, USA, August 1995.
Stilman, B., (1996a) Network Languages for Intelligent Control, An International Journal: Computers & Mathematics with Applications, (91–118), 31(3).
Stilman, B., (1996b) Network Languages for Concurrent Multiagent Systems, An International journal: Computers & Mathematics with Applications., (to appear).
Stilman, B., (1996c) From Serial to Concurrent Motions in Multiagent Systems: A Linguistic Geometry Approach, Journal of Systems Engineering, (to appear).
Yakhnis, V., Stilman, B., (1995a) Foundations of Linguistic Geometry: Complex Systems and Winning Conditions, SYMPOSIUM ON LINGUISTIC GEOMETRY AND SEMANTIC CONTROL, Proc. of the First World Congress on Intelligent Manufacturing: Processes and Systems, (843–854), Mayaguez, Puerto Rico, Feb. 1995.
Yakhnis, V., Stilman, B., (1995b) A Multi-Agent Graph-Game Approach to Theoretical Foundations of Linguistic Geometry, Proceedings of the Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI 95), Paris, France, July 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stilman, B. (1996). Linguistic Geometry tools generate optimal solutions. In: Eklund, P.W., Ellis, G., Mann, G. (eds) Conceptual Structures: Knowledge Representation as Interlingua. ICCS 1996. Lecture Notes in Computer Science, vol 1115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61534-2_5
Download citation
DOI: https://doi.org/10.1007/3-540-61534-2_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61534-7
Online ISBN: 978-3-540-68730-6
eBook Packages: Springer Book Archive