Information Technology Reference
In-Depth Information
Fig. 1.5.
Sciences making up cognitive science and links between them. Source: developed
on the basis of [6], [24]
The history of cognitive science has seen the gradual introduction of new prob-
lems represented by novel mathematical forms into this science [8], [119], [155],
[157].
The use of mathematical tools in cognitive science boiled down to two catego-
ries which could be referred to as analytical and semantic mathematics [87].
Mathematical structures based on analyzing variable functions and operations
were used to build system architectures analysing data in dynamic processes.
The analysis of this type of events led to distinguishing a new branch on the
border of cognitive informatics, computational intelligence, software engineering,
knowledge engineering and the application of mathematical forms of definitions
of the analysed problems. In recent years, Wang has called this field denotational
mathematics [142]-[144]. The key forms and structures of the mathematics created
by Wang are:
•
the notion of algebra;
•
the system of algebra;
•
the algebra of real time processes;
•
the semantic algebra.
These four basic types of mathematical structures are used in practice to exe-
cute tasks not just in the area of cognitive informatics, but also in computational
intelligence or knowledge engineering.
