dualities. There are several ways that on might try to approach this. I think that a promising one is to implement the categorification of space of problem solving (CSPS) and functions on the space (CFSPS) and to use CSPS/ CFSPS duality backwards. 

## References

Ganter, B., Wille, Rudolf, 1998. Formal Concept Analysis: Mathematical *Foundations*, Springer- Verlag, Berlin. Ganter, B., Stumme, G., Wille, R., eds., 2005. Formal Concept Analysis: Foundations and Applications, Lecture Notes in Artificial Intelligence, no. 3626, Springer-Verlag. Novak, J,. Canas, A., 2006. The Theory Underlying Concept Maps and How To Construct and Use Them, Institute for Human and Machine Cognition. Accessed 24 Nov 2008. Sowa, J., 1976, Conceptual Graphs for a Data Base Interface, IBM Journal of Research and Development 20(4), 336 357. Steyvers, M.; Tenenbaum, J.B., 2005. The Large-Scale Structure of Semantic Networks: Statistical Analyses and a Model of Semantic Growth, *Cognitive Science* 29 (1), 41 78.

Gruber, Thomas R. 1992. A Translation Approach to Portable Ontology Specifications. *Knowledge* Systems Laboratory September 1992 Technical Report KSL 92-71. Goguen, J.A. 1989. A categorical manifesto. Technical report. *SRI International, SRI-CSL-89-8.* Cadish, B., Diskin, Z. 1995. Algebraic Graph-Oriented = Category-Theory-Based. *NGITS'95 Workshop.* Ontology. 2008, Encyclopedia of Database *Systems*, Ling Liu and M. Tamer Ozsu (Eds.), Springer-Verlag, 2008.

Smith, B. 2004. Normalizing Medical Ontologies using Basic Formal Ontology, in Kooperative Versorgung, Vernetzte Forschung, Ubiquitare *Information* (Proceedings of GMDS Innsbruck, 26 30 September 2004), Niebull: Videel OHG, 199 201.

Spear, A. 2006. Ontology for the Twenty First Century: An Introduction with *Recommendations*, IFOMI, Saarbrucken, Germany.

Wikipedia, 2009, the free encyclopedia. Gruber, Thomas R., 1993. Toward Principles for the Design of Ontologies Used for Knowledge Sharing. In. Technical Report KSL 93-04, Knowledge Systems *Laboratory,* Stanford University. Feynman R, Leighton R, and Sands M., 1989. *The Feynman Lectures on Physics*, 3 volumes. Landau L. D., Lifshitz E. M. 1995. Mechanics and *Electrodynamics*. Hardcover, Elsevier Science
& Technology. Hawking S., Ellis G., Landshoff P., Nelson D., Sciama D., Weinberg S. 1975. The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics. Gabriel, P., Roiter, A. 1992. *Representations of Finite-Dimensional Algebras*, Springer-Verlag.

Drozd Yu.A., V.V. Kirichenko V.V., 1980. Finite Dimensional *Algebras*, Vyscha shkola, Kiev. Roiter A.V., Representations of marked quivers, E-print http://arXiv.org/abs/math.RT/0112158. Kent Robert E., 2002. The IFF Category Theory Ontology. Polchinski, J., 1998. *String theory* I, Cambridge Univ. Press, Cambridge.

Wess J., Bagger J., 1983. Supersymmetry *and supergravity,* Princeton Univ. Press. Glazunov, N., 2008a. Homological and Homotopical Algebra of Supersymmetries and Integrability to String Theory, Proceedings of Int. Workshop New Trends in Science and Technology
(NTST08)). http://ntst08.cankaya.edu.tr/proceedings/
Glazunov, N., 2008b. Homological and Homotopical Algebra of Supersymmetries and Integrability to String Theory (introduction and preliminaries). *E-print. arXiv: 0805.4161* Glazunov, N., 2007. Object-Oriented Knowledge Base System for Reasoning About OWL- Ontologies. Final *Scientific Report*. Kiev. 2007.

Glazunov, N., 2007. Semantic Web and Category Theory Models. Proc. Int. Seminar *Discrete* Mathematics and its Applications . Moscow: MGU (2007) P.309-311.

Glazunov, N., 2006. ategory Theory Models of Discrete Control Systems. Seventh *International* Conference Discrete Models in the Theory of Control *Systems*, Moscow Lomonosov State University, Russia, 4-6 March 2006.

Glazunov, N., Borovik, V. 2009. Databases in document-information *sphere*, Nation al Aviation Univ., Kiev.