Categorical Computing Systems

V. Gritsak-Groener, Juliya Gritsak-Groener

Abstract


This paper is the second (first see [1]) in a series whose goal is to develop a fundamentally new way of constructing theories of cacomputing (categorical computing). The motivation comes from a desire to address certain deep issues that arise when contemplating quantum and mathematical biology’s’ theories of space and time. A topos is special type of the category. The topos approach to the formulation of informatics’ theories includes a new form of informatics’ logic. We present this topos informatics’ logic, including some new results, and compare it to standard intuitionistic logic, all with an eye to conceptual issues. Importantly, topos informatics’ logic comes with a clear geometrical underpinning.


Keywords


computing; category; topos

Full Text:

PDF

References


Gritsak–Groener V. V., Gritsak–Groener Julia. A Categorical Model of Neurosystem // Proceedings of the 1996 International Conference on Parallel and Distributed Processing Techniques and Applications, Sunnnyvale Hilton, California, USA, August 9-11. — 1996. — P. 1610–1613.

Gritsak–Groener V. V. Logics and Category Theory for Natural Science- Kyjiv: SVITOZIR -ACADEMIA, 1995.-322 p.

Gritsak–Groener V. V., Gritsak–Groener Julia. Art Combinatoria

Gritsak–Groener V. V., Proceedings of AN Ukraine, 1988, N2

Gritsak–Groener V. V., Foundations of Mathematical Cybernetics,vol.1, 2004.

Gritsak–Groener V. V., Foundations of Mathematical Cybernetics,vol.2, 2005.

Valery V.Gritsak–Groener, Julia Gritsak–Groener, Hamid R. Arabnia, Modern Mathematical Biology, 2006.


Refbacks

  • There are currently no refbacks.