Artificial Intelligence pp 29-64 | Cite as

# Mathematical Foundation of Cognitive Computing Based Artificial Intelligence

## Abstract

Today Cognitive computing and Artificial Intelligence (AI) face the same challenges namely, simulate human thought processes and mimic the way human brain works. The main difference between Cognitive computing and AI is: (i) AI models various functions of human intelligence, where computer is one of the modelling means though often the most important one, i.e. intelligence is in the focus while (ii) Cognitive computing models human thought processes and simulates the hypothetical way human brain works as computation.

Our aim is to develop a theoretically and methodologically well-founded theory of AI together with a unified computational theory, which will provide specific tools and methods for Cognitive computing.

To achieve our goal we follow a methodology triangle, consisting of a conceptual-philosophical, a system theoretical and a logical-mathematical component. Computing will play a fundamental role in both system-theoretical and logical-mathematical methodological components.

Hereby we concentrate on the development of the logical-mathematical foundation in detail by the use of category theory, which provides an excellent frame for defining all notions necessary for developing a universal theory for computing, specification, cognitive reasoning, information, knowledge and their various combinations. Foundation theory is by the use of the so-called constitutions, the mathematical basis for the cognitive computation. Logical foundation will be developed as a special constitution and cognitive computing processes are defined by using situations, infons and information. The main properties are discussed with some examples.

## Keywords

Categorical theoretical foundation Cognitive computing Specification theory Cognitive reasoning Computing theory Logic programming## References

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