Induction and the rule of succession through a possibilistic inferential model lens

2026-08-12

AI Summary

This study addresses the lack of logical necessity in inductive reasoning and inherent limitations of Bayesian approaches by introducing, for the first time, a Possibilistic Inferential Model to classical inductive problems. Integrating non-probabilistic uncertainty modeling with inductive logic, the proposed framework translates empirical observations into knowledge representations endowed with statistical reliability guarantees. Applied to canonical cases such as the sunrise problem, this approach not only circumvents fundamental criticisms of Bayesian succession rules but also yields solutions that are both theoretically rigorous and practically robust. The work establishes a novel paradigm for inductive inference that eschews dependence on prior distributions while ensuring frequentist calibration.

Abstract

Induction is the process by which empirical evidence is transformed to knowledge. Hume famously argued---and Popper and others agree---that there can be no logical justification for induction. A weaker form of induction, due to Bayes, expresses the aforementioned knowledge in terms of probabilities, and we review some well-known and not-so-well-known criticisms of the Bayesian solution. We then investigate the relatively new possibilistic inferential model (IM) framework, showing that, in addition to the IM's strong, statistical reliability guarantees that it uniquely enjoys, it is safe from those criticisms that damage the Bayesian foundations. For illustration, we reconsider the classical sunrise problem and compare our proposed solution with Laplace's famous rule of succession.

Problem

• induction
• rule of succession
• Bayesian inference
• possibilistic inferential model
• sunrise problem

Innovation

• possibilistic inferential model
• induction
• rule of succession
• Bayesian criticism
• statistical reliability