A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning

Ola Hössjer, Daniel Andrés Díaz-Pachón, J. Sunil Rao

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 (Formula presented.) : 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 ((Formula presented.)), or the strength of belief in a false proposition has decreased ((Formula presented.)). 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.

Original languageEnglish (US)
Article number1469
JournalEntropy
Volume24
Issue number10
DOIs
StatePublished - Oct 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 by the authors.

Keywords

  • Bayes’ rule
  • active information
  • counterfactuals
  • epistemic probability
  • knowledge acquisition
  • learning, justified true belief
  • replication studies

PubMed: MeSH publication types

  • Journal Article

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