Glossary (en)‎ > ‎

Mathematical stratum of the GTI

Article
 
 Editor
Burgin, Mark
 Incorporated contributions
Burgin (2/2011)
 Usage domain
GTI
 Type
Theory
 French
La strate mathématique de la TGI
 German Die mathematische Schicht der GTI
 
The mathematical stratum of the General Theory of Information (GTI) builds mathematical models of information, information processes and information processing systems. According to the basic principles of GTI, information is intrinsically related to transformations. That is why portions of information are modeled by information operators in infological system representation spaces or simply in information spaces. Informally, an information space is a space where information functions (acts). In the formalized approach, information spaces are constructed as state or phase spaces of infological systems. It is possible to use different mathematical structures for state/phase representation. Thus, the mathematical stratum of the GTI is build as an operator theory in information spaces based on principles of this theory, which are translated into postulates and axioms.

There are two types of mathematical models of information: (1) information processes and (2) information processing systems. This separation results in two approaches: functional and categorical

In the functional approach, the information space is represented by functional spaces, such as Hilbert spaces or Banach spaces, while portions of information are modeled by operators in these spaces.

In the categorical approach, information spaces are represented by abstract categories (Burgin 2010b). There are two forms of information dynamics depiction in categories: the categorical and functorial representations. The categorical representation of information dynamics preserves internal structures of information spaces associated with infological systems as their state or phase spaces. In it, portions of information are modeled by categorical information operators. The functorial representation of information dynamics preserves external structures of information spaces associated with infological systems as their state or phase spaces. In it, portions of information are modeled by functorial information operators.
 
References
  • BURGIN, M. (2010a). Theory of Information: Fundamentality, Diversity and Unification. Singapore: World Scientific Publishing.
  • BURGIN, M. (2010b). Information Operators in Categorical Information Spaces. Information, 1(1), 119-152. [Online] http://www.mdpi.com/2078-2489/1/2/119/ [Accessed: 27/02/2011]
Entries
New entry. For doing a new entry: (1) the user must be identified as an authorized user(to this end, the "sign inlink at the page bottom left can be followed). (2) After being identified, press the "edit page" button at he upper right corner. (3) Being in edition mode, substitute -under this blue paragraph- "name" by the authors' names, "date" by the date in which the text is entered; and the following line by the proposed text. At the bottom of the entry, the used references in the proposed text must be given using the normalized format. (4) To finish, press the "save" button at the upper right corner.
The entry will be reviewed by the editor and -at least- another peer, and subsequently articulated in the article if elected. 

Name (date)
 
[Entry text]



Incorporated entries

Whenever an entry is integrated in the article (left column) the corresponding entry is reflected in this section.

Burgin (02/2011)

[It corresponds to the current wording of the article directly edited by the author/editor at the right column]
Comments