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$% I. Vajda, A. Veselý, and J. Zvárová, On the Amount of information resulting from
empirical and theoretical knowledge, Rev. Mat. Complut. 18 (2005), no. 2, 275–283.%$

On the Amount of Information Resulting from Empirical and Theoretical Knowledge

Igor VAJDA, Arnošt V
ESELÝ,

and Jana ZVÁROVÁ

and Jana ZVÁROVÁ

EuroMISE Center

Institute of Computer Science

Academy of Sciences of the Czech Republic

CZ-182 07, Prague — Czech Republic

Institute of Computer Science

Academy of Sciences of the Czech Republic

CZ-182 07, Prague — Czech Republic

Accepted: November 11, 2004

ABSTRACT

We present a mathematical model allowing formally define the concepts of empirical and theoretical knowledge. The model consists of a finite set of predicates and a probability space over a finite set called ontology which consists of objects for which the predicates are either valid () or not valid (). 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 are valid on the objects to some degree (). 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.