Document Type : Research Paper
Author
Computer Center, University of Baghdad
Abstract
The article gives a definition of the concept of a modified category and formulates the problem of developing a theory of modified categories that opens the way to building high-performance brain-like computers of parallel action. Analyzing the structure of the category, we discovered in it some abnormality, which gave rise to a correction of the classical category concept. Having developed such an adjustment, we received a modified category, which seems to be better for the theoretical construction starting point role of the parallel action brain-like computers basis creation. We characterize the classical category, after that we will realize its predicate interpretation. As a result, we obtain a predicate category one of the special cases of classical category. Any algebra, satisfying all the above requirements, will be regarded as an objectless classical category. It is possible to develop a theory of modified categories in parallel with the theory of classical categories. The theory of modified categories will prove to be an interesting object for theoretical research and an important tool for practical applications. It turns out that the diagrams of the theory of modified categories after their predicate interpretation coincide with the logical networks of brain-like computers. This gives us hope that the theory of modified categories will eventually become the theoretical basis for constructing of brain-like computers of parallel action.
Keywords
Main Subjects
- McLane S.(2004). "Categories for the working mathematician".P.349.2nd edition, Springer, USA.
- S. Abramsky, N. Tzevelekos (2011). "Introduction to Categories and Categorical Logic". P.178, 1st. edition, Springer, Germany.
- J. Adamek, H. Herrlich, G.E. Strecker(1990). "Abstract and concrete categories. The joy of cats". P.225 1st edition, Wiley, USA.
- S. Awodey(2010). "Category theory", 2nd edition. Oxford University Press, UK.
- M. Barr, C. Wells (1990). "Category Theory for Computing Science". Prentice Hall, USA.
- F. Borceaux. "Handbbook of categorical algebra, v.1. Basic category theory". Cambridge University Press, UK.
- A. Schalk, H. Simmons (2005). "An introduction to category theory in four easy movements", University of Manchester, UK.
- Boggs, M., Boggs, W.(1999). "Mastering UML with relational rose", P.510, Sybex; Pap/Cdr edition, UK.
- Bondarenko MF, Shabanov-Kushnarenko Yu.P.(2007). "The theory of intelligence", P.576, Textbook. Kharkiv. The SMIT Publishing House. Ukraine.
- Leshchinskaya I.A.(2010). "Linear logical operators of the first and second kind in relational networks ", P. 214-217, Control, navigation and communication systems", №2 (14), Ukraine.
- Leshchinskaya IA, Leshchinsky VA, Tokarev VV, Chetverikov G.G.(2006). "Synthesis of binary logical networks and features of their functioning ", Bionics of the intellect, P.14-18, №2 (65), Ukraine.
- Leshchinskaya I.A.(2010). "The method of constructing directed schemes of relational networks using the example of the equivalence relation ", Information processing system, P. 75-81, No. 1 (82), Ukraine.
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