Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-2767-8818
Number of Authors: 32022 (English)In: Entropy, E-ISSN 1099-4300, Vol. 24, no 10, article id 1469Article in journal (Refereed) Published
Abstract [en]

Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes’ rule. The degree of true belief is quantified by means of active information I+: a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent’s strength of belief in a true proposition has increased in comparison with the ignorant person (I+>0), or the strength of belief in a false proposition has decreased (I+<0). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus.

Place, publisher, year, edition, pages
2022. Vol. 24, no 10, article id 1469
Keywords [en]
active information, Bayes' rule, counterfactuals, epistemic probability, learning, justified true belief, knowledge acquisition, replication studies
National Category
Computer and Information Sciences Mathematics Philosophy, Ethics and Religion
Identifiers
URN: urn:nbn:se:su:diva-211039DOI: 10.3390/e24101469ISI: 000872645400001Scopus ID: 2-s2.0-85140609692OAI: oai:DiVA.org:su-211039DiVA, id: diva2:1709698
Available from: 2022-11-09 Created: 2022-11-09 Last updated: 2023-03-28Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records

Hössjer, Ola

Search in DiVA

By author/editor
Hössjer, Ola
By organisation
Department of Mathematics
In the same journal
Entropy
Computer and Information SciencesMathematicsPhilosophy, Ethics and Religion

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 44 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf