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A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning
Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.ORCID-id: 0000-0003-2767-8818
Antal upphovsmän: 32022 (Engelska)Ingår i: Entropy, E-ISSN 1099-4300, Vol. 24, nr 10, artikel-id 1469Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2022. Vol. 24, nr 10, artikel-id 1469
Nyckelord [en]
active information, Bayes' rule, counterfactuals, epistemic probability, learning, justified true belief, knowledge acquisition, replication studies
Nationell ämneskategori
Data- och informationsvetenskap Matematik Filosofi, etik och religion
Identifikatorer
URN: urn:nbn:se:su:diva-211039DOI: 10.3390/e24101469ISI: 000872645400001Scopus ID: 2-s2.0-85140609692OAI: oai:DiVA.org:su-211039DiVA, id: diva2:1709698
Tillgänglig från: 2022-11-09 Skapad: 2022-11-09 Senast uppdaterad: 2023-03-28Bibliografiskt granskad

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Hössjer, Ola

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Data- och informationsvetenskapMatematikFilosofi, etik och religion

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