Probabilistic Logics and Probabilistic Networks

Description

While probabilistic logics in principle might be applied to solve a range of problems, in practice they are rarely applied --- perhaps because they seem disparate, complicated, and computationally intractable. This programmatic book argues that several approaches to probabilistic logic fit into a simple unifying framework in which logically complex evidence is used to associate probability intervals or probabilities with sentences. Specifically, Part I shows that there is a natural way to present a question posed in probabilistic logic, and that various inferential procedures provide semantics for that question, while Part II shows that there is the potential to develop computationally feasible methods to mesh with this framework. The book is intended for researchers in philosophy, logic, computer science and statistics. A familiarity with mathematical concepts and notation is presumed, but no advanced knowledge of logic or probability theory is required. Front Matter....Pages i-xiii Front Matter....Pages 1-1 Introduction....Pages 3-10 Standard Probabilistic Semantics....Pages 11-20 Probabilistic Argumentation....Pages 21-31 Evidential Probability....Pages 33-48 Statistical Inference....Pages 49-61 Bayesian Statistical Inference....Pages 63-71 Objective Bayesian Epistemology....Pages 73-82 Front Matter....Pages 83-83 Credal and Bayesian Networks....Pages 85-97 Networks for the Standard Semantics....Pages 99-105 Networks for Probabilistic Argumentation....Pages 107-110 Networks for Evidential Probability....Pages 111-117 Networks for Statistical Inference....Pages 119-124 Networks for Bayesian Statistical Inference....Pages 125-131 Networks for Objective Bayesianism....Pages 133-137 Conclusion....Pages 139-139 Back Matter....Pages 141-155