A decidable class of inferences in first-order objective Bayesian inductive logic
Abstract
We show that while standard first-order inductive logic is not decidable, a large class of inferences in objective Bayesian inductive logic is decidable. Decidability is achieved by reducing the general inference problem to a quantifier-free problem. We show that for any inference, if the quantifier-free reduction of the premisses is satisfiable, then the original inference is decidable. We go on to show that Bayesian networks offer the potential to provide a computationally tractable inference procedure for objective Bayesian inductive logic. We also consider inferences with infinitely many premisses and explore some properties of the logic.
Fields of Study & Subjects
Logic
Reasoning
and Knowledge
Bayesian Modeling and Causal Inference
Philosophy and History of Science
Publication details
- Journal / source
- Annals of Pure and Applied Logic
- Volume
- 177
- Issue
- 6
- Pages
- 103714–103714
- Publication date
- 7 January 2026
- Language
- EN