Foundations of AIT
Algorithmic Information Theory explores the relationship between computation and information. Its foundational metric is Kolmogorov Complexity, which defines the information content of an object as the length of the shortest program required to produce it.
Core Mathematical Principles
- Universal Induction (Solomonoff): A theory of prediction that uses Kolmogorov complexity to assign prior probabilities to future events.
- Minimum Description Length (MDL): A principle stating that the optimal model for a dataset is the one that minimizes the description length of the model plus the data compressed relative to that model.
- Chaitin's Constant (Ω): A real number that represents the probability that a randomly constructed program will halt, embodying the limits of formal verification.
- Bennett's Logical Depth: A measure of complexity based on the computational time required to calculate an object from its shortest compressed description.
- Algorithmic Probability: Assigning higher probability to data strings that can be generated by shorter computer programs.
Theoretical Objective
AIT principles are utilized to evaluate the efficiency of reasoning systems. Within an agentic framework, the objective is to minimize the complexity of logical explanations for observed data, favoring models that achieve higher levels of algorithmic compression.