Information is usually related to knowledge. Here, we present a broader picture in which information is associated with epistemic structures, which form cognitive infological systems as basic recipients and creators of cognitive information. Infological systems are modeled by epistemic spaces, while operators in these spaces are mathematical models of information. Information that acts on epistemic structures is called cognitive information, while information that acts on knowledge structures is called epistemic information. The latter brings new and updates existing knowledge, being of primary importance to people. In this paper, both types of information are studied as operators in epistemic spaces based on the general theory of information. As a synthetic approach, which reveals the essence of information, organizing and encompassing all main directions in information theory, the general theory of information provides efficient means for such a study. Different types of information dynamics representation use tools from various mathematical disciplines, such as the theory of categories, functional analysis, mathematical logic and algebra. In this paper, we base our exploration of information and knowledge dynamics on functional analysis further developing the mathematical stratum of the general theory of information.

Information is usually related to knowledge. However, the recent development of information theory demonstrated that information is a much broader concept, being actually present in and virtually related to everything. As a result, many unknown types and kinds of information have been discovered. Nevertheless, information that acts on knowledge, bringing new and updating existing knowledge, is of primary importance to people. It is called epistemic information, which is studied in this paper based on the general theory of information and further developing its mathematical stratum. As a synthetic approach, which reveals the essence of information, organizing and encompassing all main directions in information theory, the general theory of information provides efficient means for such a study. Different types of information dynamics representation use tools of mathematical disciplines such as the theory of categories, functional analysis, mathematical logic and algebra. Here we employ algebraic structures for exploration of information and knowledge dynamics. In Introduction (Section 1), we discuss previous studies of epistemic information. Section 2 gives a compressed description of the parametric phenomenological definition of information in the general theory of information. In Section 3, anthropic information, which is received, exchanged, processed and used by people is singled out and studied based on the Componential Triune Brain model. One of the basic forms of anthropic information called epistemic information, which is related to knowledge, is analyzed in Section 4. Mathematical models of epistemic information are studied in Section 5. In Conclusion, some open problems related to epistemic information are given.

Evolutionary information theory is a constructive approach that studies information in the context of evolutionary processes, which are ubiquitous in nature and society. In this paper, we develop foundations of evolutionary information theory, building several measures of evolutionary information and obtaining their properties. These measures are based on mathematical models of evolutionary computations, machines and automata. To measure evolutionary information in an invariant form, we construct and study universal evolutionary machines and automata, which form the base for evolutionary information theory. The first class of measures introduced and studied in this paper is evolutionary information size of symbolic objects relative to classes of automata or machines. In particular, it is proved that there is an invariant and optimal evolutionary information size relative to different classes of evolutionary machines. As a rule, different classes of algorithms or automata determine different information size for the same object. The more powerful classes of algorithms or automata decrease the information size of an object in comparison with the information size of an object relative to weaker4 classes of algorithms or machines. The second class of measures for evolutionary information in symbolic objects is studied by introduction of the quantity of evolutionary information about symbolic objects relative to a class of automata or machines. To give an example of applications, we briefly describe a possibility of modeling physical evolution with evolutionary machines to demonstrate applicability of evolutionary information theory to all material processes. At the end of the paper, directions for future research are suggested.

Based on the general theory of information (GTI), we study ontological information, which is complementary to the concept of mental information in general and epistemic information in particular.

This paper has a two-fold goal. In the first part, the area of theoretical and foundational information studies is delineated. In the second part, the general overview of the conference “Theoretical and Foundational Problems in Information Studies” (TFP) is given.

Concepts play an important role in human culture, forming explicit and implicit conceptual spaces. The goal of this paper is to explore the structural organization of information in conceptual spaces.