2020/05/03 by Hiroyuki Kido, Kido, Hiroyuki
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Decision-Making and Behavioral Economics #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Machine Learning (cs.LG)
paper · pdf · doi:10.48550/arxiv.2005.00961
openalex publication_date 2020/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to another hypothesis that there is a Bayesian algorithm and data-structure for logical reasoning. In this paper, we give a Bayesian account of entailment and characterize its abstract inferential properties. The Bayesian entailment is shown to be a monotonic consequence relation in an extreme case. In general, it is a sort of non-monotonic consequence relation without Cautious monotony or Cut. The preferential entailment, which is a representative non-monotonic consequence relation, is shown to be maximum a posteriori entailment, which is an approximation of the Bayesian entailment. We finally discuss merits of our proposals in terms of encoding preferences on defaults, handling change and contradiction, and modeling human entailment.