A Formal Framework for Knowledge Acquisition: Going beyond Machine Learning.

Area of Science:

• Epistemology
• Mathematical Logic
• Decision Theory

Background:

• Philosophical definitions of knowledge often cite justified, true belief.
• Existing frameworks lack precise mathematical definitions for learning and knowledge acquisition.
• Belief is often treated qualitatively, hindering quantitative analysis.

Purpose of the Study:

• To develop a precise mathematical framework for defining learning and knowledge acquisition.
• To quantify the degree of true belief using a novel metric.
• To differentiate between machine learning and genuine knowledge acquisition.

Main Methods:

• Formulating belief in terms of epistemic probabilities derived from Bayes' rule.
• Quantifying the degree of true belief using active information (I+).
• Introducing a parallel worlds framework to model hypothesis testing and parameter estimation.

Main Results:

• Learning is defined as an increase in true beliefs (I+>0) or decrease in false beliefs (I+<0).
• Knowledge acquisition requires learning for the correct reasons, involving true world parameter estimation.
• The framework integrates frequentist and Bayesian approaches, applicable in sequential settings.

Conclusions:

• The proposed framework offers a rigorous, hybrid approach to understanding learning and knowledge.
• It provides a basis for analyzing and potentially improving machine learning algorithms.
• The model elucidates the distinction between mere learning and true knowledge acquisition.