ALGEBRAIC STRUCTURE OF KNOWLEDGE TRANSFER MODEL
This paper is an extension of the work originally presented in conference ICERI2019 . We presented the way of understanding the relation of information and knowledge by showing that knowledge is built on previous acquired knowledge, that is just as information in new relation. We find that we have to define mathematical model using algebraic structure to describe this phenomena.
In educational sense we use this as model to give new paradigm in education, we suggest that education should enable students to find relations from knowledge that they acquire and the teacher should use different models (functions) to classify knowledge and enable students to discover (using class of functions) new knowledge. That model will help to develop self-adapting system for autonomous learning (new algorithms) what we have found out that we need in times we live today.
The interpretation of knowledge given in this paper gives us an opportunity to develop different algorithms for acquiring knowledge which is independent from its type, just by defining the function for transforming the set of information. This gives us the opportunity to interpret newly acquired knowledge as information for further interpretation and acquisition of different knowledge. In this paper, we go further in abstracting the knowledge and knowledge representation and show the model that can explain how new knowledge can be acquired from similar but not the same set of information.
Entering into the realm of groups is necessary for the mapping from a set of information to a set of knowledge to be an analytic function, which opens the possibility for us to abstract such a function by a polynomial, for example, a Taylor polynomial, which will greatly facilitate our knowledge transfer.
In the analysis of knowledge transfer, particular attention should be paid to the domain of function or set of information. A set of information consists of a series of subsets that form a partitive set of domains. One of the characteristics of a partition of a set (the set of all subsets) is its cardinal number, the Bell number.
The property we have shown here may be another approach in the development of artificial intelligence, for which it is necessary to mathematically represent developments in the creation of a set of knowledge.
This model helps us understand the knowledge creation in different disciplines and from different fields of work