{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:28:13Z","timestamp":1760243293922,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T00:00:00Z","timestamp":1402444800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/info5020357","type":"journal-article","created":{"date-parts":[[2014,6,11]],"date-time":"2014-06-11T11:59:22Z","timestamp":1402487962000},"page":"357-388","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Weighted E-Spaces and Epistemic Information Operators"],"prefix":"10.3390","volume":"5","author":[{"given":"Mark","family":"Burgin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California, 405 Hilgard Ave., Los Angeles, CA 90095, USA"}]}],"member":"1968","published-online":{"date-parts":[[2014,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Burgin, M. (2010). Theory of Information: Fundamentality, Diversity and Unification, World Scientific.","DOI":"10.1142\/7048"},{"key":"ref_2","unstructured":"Burgin, M. (2011). Theory of Named Sets, Nova Science Publishers."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"697","DOI":"10.3390\/info2040697","article-title":"Epistemic information in stratified M-spaces","volume":"2","author":"Burgin","year":"2011","journal-title":"Information"},{"key":"ref_4","unstructured":"Mizzaro, S. (2001). Information Modelling and Knowledge Bases, IOS Press."},{"key":"ref_5","first-page":"48","article-title":"Information and transformation","volume":"10","author":"Burgin","year":"1998\/1999","journal-title":"Transformation"},{"key":"ref_6","unstructured":"Burgin, M. (2012). Structural Reality, Nova Science Publishers."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Frieden, R.B. (1998). Physics from Fisher Information, Cambridge University Press.","DOI":"10.1017\/CBO9780511622670"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1515\/zna-1958-0401","article-title":"Die Quantentheorie der einfachen Alternative (Komplementarit\u00e4t und Logik, II)","volume":"13","year":"1958","journal-title":"Z. Naturforsch."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1515\/zna-1958-0901","article-title":"Komplementarit\u00e4t und Logik, III (Mehrfache Quantelung)","volume":"13","author":"Scheibe","year":"1958","journal-title":"Z. Naturforsch."},{"key":"ref_10","unstructured":"Zurek, W. (1990). Complexity, Entropy, and the Physics of Information, Addison-Wesley."},{"key":"ref_11","first-page":"155","article-title":"Information in the context of education","volume":"14","author":"Burgin","year":"2001","journal-title":"J. Interdiscip. Stud."},{"key":"ref_12","first-page":"147","article-title":"Semantic information","volume":"4","author":"Carnap","year":"1958","journal-title":"Br. J. Philos. Sci."},{"key":"ref_13","first-page":"205","article-title":"The Varieties of Information and Scientific Explanation","volume":"Volume 5","author":"Hintikka","year":"1999","journal-title":"Inquiry as Inquiry: A Logic of Scientific Discovery"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/978-94-010-3296-4_8","article-title":"Surface Information and Depth Information","volume":"Volume 28","author":"Hintikka","year":"1970","journal-title":"Information and Inference"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0020-0271(65)80003-1","article-title":"On the semantic characteristics of information","volume":"2","author":"Shreider","year":"1965","journal-title":"Inf. Storage Retr."},{"key":"ref_16","unstructured":"Anderson, R.C., Spiro, R.J., and Montague, W.E. (1977). Schooling and the Acquisition of Knowledge, Lawrence Erlbaum."},{"key":"ref_17","unstructured":"Arbib, M. (1992). The Encyclopedia of AI, Wiley-Interscience."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1207\/s15326985ep2104_2","article-title":"Schema Theory and the design of content-area textbooks","volume":"21","author":"Armbruster","year":"1996","journal-title":"Educ. Psychol."},{"key":"ref_19","unstructured":"Barwise, J., and Perry, J. (1983). Situations and Attitudes, MIT Press."},{"key":"ref_20","unstructured":"Burgin, M., and Bratalskii, E.A. (1986). Operation Research and Automated Control Systems, Naukova Dumka. (in Russian)."},{"key":"ref_21","first-page":"80","article-title":"The language PDL for the large system design automation","volume":"5","author":"Burgin","year":"1979","journal-title":"Progr. Comput. Softw."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Ganter, B., and Wille, R. (1999). Formal Concept Analysis\u2014Mathematical Foundations, Springer.","DOI":"10.1007\/978-3-642-59830-2"},{"key":"ref_23","unstructured":"Chalmers, D.J. (2011). Epistemic Modality, Oxford University Press."},{"key":"ref_24","unstructured":"Burgin, M. (2004, January 9\u201311). Logical tools for program integration and interoperability. Proceedings of the IASTED International Conference on Software Engineering and Applications, MIT, Cambridge, MA, USA."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"065102","DOI":"10.1103\/PhysRevE.65.065102","article-title":"Topology of the conceptual network of language","volume":"65","author":"Motter","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_26","unstructured":"Kuratowski, K. (1966). Topology, Academic Press."},{"key":"ref_27","unstructured":"Burgin, M. (2005). Super-Recursive Algorithms, Springer."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"G\u00e4rdenfors, P. (2000). Conceptual Spaces: On the Geometry of Thought, MIT Press.","DOI":"10.7551\/mitpress\/2076.001.0001"},{"key":"ref_29","first-page":"9","article-title":"Conceptual spaces as a framework for knowledge representation","volume":"2","year":"2004","journal-title":"Mind Matter"},{"key":"ref_30","unstructured":"Osgood, C.E., Suci, G.J., and Tannenbaum, P.N. (1967). The Measurement of Meaning, University of Illinois Press."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Bourbaki, N. (1987). Topological Vector Spaces, Elements of Mathematics, Springer.","DOI":"10.1007\/978-3-642-61715-7"},{"key":"ref_32","unstructured":"Le Potier, J. (1997). Lectures on Vector Bundles, Cambridge University Press. Cambridge Studies in Advanced Mathematics."},{"key":"ref_33","first-page":"1","article-title":"Semitopological vector spaces and hyperseminorms","volume":"3","author":"Burgin","year":"2013","journal-title":"Theory Appl. Math. Comput. Sci."},{"key":"ref_34","unstructured":"Rudin, W. (1991). Functional Analysis, McGrow-Hill."},{"key":"ref_35","unstructured":"Burgin, M., and Debnath, N. (2003, January 11\u201313). Hardship of program utilization and user-friendly software. Proceedings of the ISCA 16th International Conference on Computer Applications in Industry and Engineering (CAINE-2003)International Society for Computers and their Applications, Las Vegas, NV, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s11787-006-0007-2","article-title":"Information Algebras and consequence operators","volume":"1","author":"Kohlas","year":"2007","journal-title":"Log. Univers."},{"key":"ref_37","unstructured":"Shoenfield, J.R. (1967). Mathematical Logic, Addison-Wesley."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"119","DOI":"10.3390\/info1020119","article-title":"Information operators in categorical information spaces","volume":"1","author":"Burgin","year":"2010","journal-title":"Information"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Burgin, M. (2011). Information Dynamics in a Categorical Setting, in Information and Computation, World Scientific.","DOI":"10.1142\/9789814295482_0002"},{"key":"ref_40","first-page":"485","article-title":"Discontinuity structures in topological spaces","volume":"16","author":"Burgin","year":"2004","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_41","unstructured":"Alexandroff, P. (1961). Elementary Concepts of Topology, Dover Publications, Inc."},{"key":"ref_42","unstructured":"Burgin, M. (2008). Neoclassical Analysis: Calculus Closer to the Real World, Nova Science Publishers."},{"key":"ref_43","unstructured":"Dunford, N., and Schwartz, J. (1958). Linear Operators, Interscience Publishers."},{"key":"ref_44","first-page":"5","article-title":"Information Algebras","volume":"6","author":"Burgin","year":"1997","journal-title":"Control Syst. Mach."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/5\/2\/357\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:12:21Z","timestamp":1760217141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/5\/2\/357"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,11]]},"references-count":44,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,6]]}},"alternative-id":["info5020357"],"URL":"https:\/\/doi.org\/10.3390\/info5020357","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2014,6,11]]}}}