On the amount of information resulting from empirical and theoretical knowledge.

Igor Vajda; Arnost Vesely; Jana Zvarova

Revista Matemática Complutense (2005)

  • Volume: 18, Issue: 2, page 275-283
  • ISSN: 1139-1138

Abstract

top
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 (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 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 π ∈ P are valid on the objects ω ∈ Ω to some degree (0 ≤ π(ω) ≤ 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.

How to cite

top

Vajda, Igor, Vesely, Arnost, and Zvarova, Jana. "On the amount of information resulting from empirical and theoretical knowledge.." Revista Matemática Complutense 18.2 (2005): 275-283. <http://eudml.org/doc/38165>.

@article{Vajda2005,
abstract = {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 (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 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 π ∈ P are valid on the objects ω ∈ Ω to some degree (0 ≤ π(ω) ≤ 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.},
author = {Vajda, Igor, Vesely, Arnost, Zvarova, Jana},
journal = {Revista Matemática Complutense},
keywords = {Teoría de la información; Bases de conocimiento; Medidas de información; Semántica; Lógica difusa},
language = {eng},
number = {2},
pages = {275-283},
title = {On the amount of information resulting from empirical and theoretical knowledge.},
url = {http://eudml.org/doc/38165},
volume = {18},
year = {2005},
}

TY - JOUR
AU - Vajda, Igor
AU - Vesely, Arnost
AU - Zvarova, Jana
TI - On the amount of information resulting from empirical and theoretical knowledge.
JO - Revista Matemática Complutense
PY - 2005
VL - 18
IS - 2
SP - 275
EP - 283
AB - 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 (Ω, S, P) over a finite set Ω called ontology which consists of objects ω for which the predicates π ∈ P are either valid (π(ω) = 1) or not valid (π(ω) = 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 π ∈ P are valid on the objects ω ∈ Ω to some degree (0 ≤ π(ω) ≤ 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.
LA - eng
KW - Teoría de la información; Bases de conocimiento; Medidas de información; Semántica; Lógica difusa
UR - http://eudml.org/doc/38165
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.