2022/02/27 by Hiroyuki Kido, Kido, Hiroyuki
Biochemistry, Genetics and Molecular Biology · Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Biomedical Text Mining and Ontologies #FOS: Computer and information sciences #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2202.13406
openalex publication_date 2022/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the likelihood, Bayes' theorem gives the posterior of the model being the case given the formula. The posterior represents an inverse interpretation of formal logic that seeks models making the formula true. The likelihood and posterior cause Bayesian learning that gives the probability of the conclusion being true in the models where all the premises are true. This paper looks at statistical and logical properties of the Bayesian learning. It is shown that the generative model is a unified theory of several different types of reasoning in logic and statistics.