ABSTRACT

      An intelligent agent interacting with the real world will encounter individual people, courses, test results, drugs prescriptions, chairs, boxes, etc., and needs to reason about properties of these individuals and relations among them as well as cope with uncertainty.

      Uncertainty has been studied in probability theory and graphical models, and relations have been studied in logic, in particular in the predicate calculus and its extensions. This book examines the foundations of combining logic and probability into what are called relational probabilistic models. It introduces representations, inference, and learning techniques for probability, logic, and their combinations.

      The book focuses on two representations in detail: Markov logic networks, a relational extension of undirected graphical models and weighted first-order predicate calculus formula, and Problog, a probabilistic extension of logic programs that can also be viewed as a Turing-complete relational extension of Bayesian networks.

       KEYWORDS

      probabilistic logic models, relational probabilistic models, lifted inference, statistical relational learning, probabilistic programming, inductive logic programming, logic programming, machine learning, Prolog, Problog, Markov logic networks

       Contents

       Preface

       1 Motivation

       1.1 Uncertainty in Complex Worlds

       1.2 Challenges of Understanding StarAI

       1.3 The Benefits of Mastering StarAI

       1.4 Applications of StarAI

       1.5 Brief Historical Overview

       PART I Representations

       2 Statistical and Relational AI Representations

       2.1 Probabilistic Graphical Models

       2.1.1 Bayesian Networks

       2.1.2 Markov Networks and Factor Graphs

       2.2 First-Order Logic and Logic Programming

       3 Relational Probabilistic Representations

       3.1 A General View: Parameterized Probabilistic Models

       3.2 Two Example Representations: Markov Logic And ProbLog

       3.2.1 Undirected Relational Model: Markov Logic

       3.2.2 Directed Relational Models: ProbLog

       4 Representational Issues

       4.1 Knowledge Representation Formalisms

       4.2 Objectives for Representation Language

       4.3 Directed vs. Undirected models

       4.4 First-Order Logic vs. Logic Programs

       4.5 Factors and Formulae

       4.6 Parameterizing Atoms

       4.7 Aggregators and Combining Rules

       4.8 Open Universe Models

       4.8.1 Identity Uncertainty

       4.8.2 Existence Uncertainty

       4.8.3 Ontologies

       PART II Inference

       5 Inference in Propositional Models

       5.1 Probabilistic Inference

       5.1.1 Variable Elimination

       5.1.2 Recursive Conditioning

       5.1.3 Belief Propagation

       5.2 Logical Inference

       5.2.1 Propositional Logic, Satisfiability, and Weighted Model Counting

       5.2.2 Semiring Inference

       5.2.3 The Least Herbrand Model

       5.2.4 Grounding

       5.2.5 Proving

       6 Inference in Relational Probabilistic Models

       6.1 Grounded Inference for Relational Probabilistic Models

       6.1.1 Weighted Model Counting

       6.1.2 WMC for Markov Logic

       6.1.3 WMC for ProbLog

       6.1.4 Knowledge Compilation

       6.2 Lifted Inference: Exploiting Symmetries

       6.2.1 Exact Lifted Inference

       6.3 (Lifted) Approximate Inference

       PART III Learning

       7 Learning Probabilistic and Logical Models

       7.1 Learning Probabilistic Models