Full paper in PDF:
$% I. Vajda, A. Veselý, and J. Zvárová, On the Amount of information resulting from empirical and theoretical knowledge, Rev. Mat. Complut. 18 (2005), no. 2, 275283.%$

On the Amount of Information Resulting from Empirical and Theoretical Knowledge

and Jana ZVÁROVÁ
EuroMISE Center
Institute of Computer Science
Academy of Sciences of the Czech Republic
CZ-182 07, Prague Czech Republic

Received: August 26, 2004
Accepted: November 11, 2004

We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set P of predicates and a probability space (_O_,S,P)  over a finite set _O_  called ontology which consists of objects w  for which the predicates p  (-  P are either valid (p(w) = 1  ) or not valid (p(w)= 0  ). Since this is a first step in this area, our approach is as simple as possible, but still nontrivial, as it is demonstrated by examples. More realistic approach would be more complicated, based on a fuzzy logic where the predicates p  (-  P are valid on the objects w  (-  _O_  to some degree (0< p(w)< 1  ). We use the classical information divergence to introduce the amount of information in empirical and theoretical knowledge. By an example is demonstrated that information in theoretical knowledge is an extension of the “sematic information” introduced formerly by Bar Hillel and Carnap as an alternative to the information of Shannon.

Key words: probability space, ontology, predicate, knowledge area, state of the knowledge area, empirical knowledge, theoretical knowledge, information in empirical knowledge, information in theoretical knowledge.
2000 Mathematics Subject Classification:
G2B10, 94A17, 94D05.