Advertisement

Introducing the mathematical category of artificial perceptions

  • Z. Arzi-Gonczarowski
  • D. Lehmann
Article

Abstract

Perception is the recognition of elements and events in the environment, usually through integration of sensory impressions. It is considered here as a broad, high-level, concept (different from the sense in which computer vision/audio research takes the concept of perception). We propose and develop premises for a formal approach to a fundamental phenomenon in AI: the diversity of artificial perceptions. A mathematical substratum is proposed as a basis for a rigorous theory of artificial perceptions. A basic mathematical category is defined. Its objects are perceptions, consisting of world elements, connotations, and a three-valued (true, false, undefined) predicative correspondence between them. Morphisms describe paths between perceptions. This structure serves as a basis for a mathematical theory. This theory provides a way of extending and systematizing certain intuitive pre-theoretical conceptions about perception, about improving and/or completing an agent's perceptual grasp, about transition between various perceptions, etc. Some example applications of the theory are analyzed.

Keywords

Choice Function Category Theory Unique Morphism Terminal Object Sensory Impression 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M.A. Arbib and E.G. Manes, Arrows, Structures and Functors–The Categorical Imperative(Academic Press, New York, 1975).Google Scholar
  2. [2]
    Z. Arzi-Gonczarowski and D. Lehmann, Categorical tools for artificial perception, in: Proceedings of the 11th European Conference on Artificial Intelligence ECAI ’94, ed. A. Cohn (Wiley, Amsterdam, 1994) pp. 757–761.Google Scholar
  3. [3]
    Z. Arzi-Gonczarowski and D. Lehmann, From environments to representations–A mathematical theory of artificial perceptions, Artificial Intelligence, forthcoming.Google Scholar
  4. [4]
    A. Asperti and G. Longo, Categories, Types, and Structures(MIT Press, 1991).Google Scholar
  5. [5]
    R.B. Banerji, Similarities in problem solving strategies, in: Change of Representation and Inductive Bias, ed. D.P. Benjamin (Kluwer Academic, 1990) pp. 183–191.Google Scholar
  6. [6]
    M. Barr and C. Wells, Category Theory for Computing Science(Prentice-Hall, Englewood Cliffs, NJ, 2nd ed., 1995).Google Scholar
  7. [7]
    E.A. Bender, Mathematical Methods in Artificial Intelligence(IEEE, Los Alamitos, CA, 1995).Google Scholar
  8. [8]
    D.P. Benjamin, A review of [31], SIGART Bulletin 3(4) (October 1992).Google Scholar
  9. [9]
    F. Borceux, Handbook of Categorical Algebra(Cambridge University Press, Cambridge, 1994).Google Scholar
  10. [10]
    R. Casati and A.C. Varzi, Basic issues in spatial representation, in: Proceedings of WOCFAI ’95, Second World Conference on the Fundamentals of AI, eds. M. DeGlas and Z. Pawlak (Angkor, Paris, 1995) pp. 63–72.Google Scholar
  11. [11]
    M.A. Croon and F.J.R. Van de Vijver, eds., Viability of Mathematical Models in the Social and Behavioral Sciences(Swets and Zeitlinger B.V., Lisse, 1994).Google Scholar
  12. [12]
    E.R. Doughherty and C.R. Giardina, Mathematical Methods for Artificial Intelligence and Autonomous Systems(Prentice-Hall, Englewood Cliffs, NJ, 1988).Google Scholar
  13. [13]
    W.D. Ellis, ed., A Source Book of Gestalt Psychology(Routledge and Kegan Paul, London, 1938).Google Scholar
  14. [14]
    N. Fridman and C.D. Hafner, The state of the art in ontology design, AI Magazine 18(3) (1997).Google Scholar
  15. [15]
    P. Gärdenfors, Induction, conceptual spaces and AI, Philosophy of Science 57 (1990) 78–95.MathSciNetCrossRefGoogle Scholar
  16. [16]
    H. Herrlich and G.E. Strecker, Category Theory(Allyn and Bacon, 1973).Google Scholar
  17. [17]
    J.P.E. Hodgson, Pushouts and problem solving, in: Working Proceedings of the First International Workshop on Category Theory in AI and Robotics, eds. I. Mandhyan, D.P. Benjamin and E.G. Manes (Philips Laboratories, 1989) pp. 89–112.Google Scholar
  18. [18]
    B. Indurkhya, Approximate semantic transference: A computational theory of metaphors and analogies, Cognitive Science 11 (1987) 445–480.CrossRefGoogle Scholar
  19. [19]
    S. Kraus and D. Lehmann, Designing and building a negotiating automated agent, Computational Intelligence 11(1) (1995) 132–171.Google Scholar
  20. [20]
    S. Kripke, Semantical considerations on modal logic, Acta Philosophica Fennica 16 (1963) 83–94.zbMATHMathSciNetGoogle Scholar
  21. [21]
    G. Lakoff, Women, Fire, and Dangerous Things–What Categories Reveal about the Mind(The University of Chicago Press, Chicago, 1987).Google Scholar
  22. [22]
    F.W. Lawvere, Tools for the advancement of objective logic: Closed categories and toposes, in: The Logical Foundations of Cognition, eds. J. Macnamara and G.E. Reyes (Oxford University Press, Oxford, 1994) pp. 43–55.Google Scholar
  23. [23]
    M.R. Lowry, Algorithm synthesis through problem reformulation, Ph.D. thesis, Stanford University (June 1989).Google Scholar
  24. [24]
    M.R. Lowry, Strata: Problem reformulation and abstract data types, in: Change of Representation and Inductive Bias, ed. D.P. Benjamin (Kluwer Academic Publishers, 1990) pp. 41–66.Google Scholar
  25. [25]
    S. MacLane, Categories for the Working Mathematician(Springer, Berlin, 1972).Google Scholar
  26. [26]
    F. Magnan and G.E. Reyes, Category theory as a conceptual tool in the study of cognition, in: The Logical Foundations of Cognition, eds. J. Macnamara and G.E. Reyes (Oxford University Press, Oxford, 1994) pp. 57–90.Google Scholar
  27. [27]
    J.A. Makowsky, Mental images and the architecture of concepts, in: The Universal Turing Machine–A Half Century Survey, ed. R. Herken (Oxford University Press, Oxford, 1988) pp. 453–465.Google Scholar
  28. [28]
    A. Newell, Unified Theories of Cognition(Harvard University Press, Cambridge, MA, 1990).Google Scholar
  29. [29]
    N.J. Nilsson, Artificial intelligence prepares for 2001, AI Magazine 4(4) (1983).Google Scholar
  30. [30]
    N.J. Nilsson, Eye on the prize, AI Magazine 16(2) (1995) 9–17.Google Scholar
  31. [31]
    B.C. Pierce, Basic Category Theory for Computer Scientists(MIT Press, 1991).Google Scholar
  32. [32]
    R.F.C. Walters, Categories and Computer Science(Cambridge University Press, Cambridge, 1991).Google Scholar
  33. [33]
    R.M. Zimmer, Representation engineering and category theory, in: Change of Representation and Inductive Bias, ed. D.P. Benjamin (Kluwer Academic Publishers, 1990) pp. 169–182.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Z. Arzi-Gonczarowski
    • 1
  • D. Lehmann
    • 2
  1. 1.Typographics LtdJerusalemIsrael
  2. 2.Institute of Computer ScienceThe Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations