Logic, Knowledge Representation, and Bayesian Decision Theory

In this paper I give a brief overview of recent work on uncertainty inAI, and relate it to logical representations. Bayesian decision theory and logic are both normative frameworks for reasoning that emphasize different aspects of intelligent reasoning. Belief networks (Bayesian networks) are representations of independence that form the basis for understanding much of the recent work on reasoning under uncertainty, evidential and causal reasoning, decision analysis, dynamical systems, optimal control, reinforcement learning and Bayesian learning. The independent choice logic provides a bridge between logical representations and belief networks that lets us understand these other representations and their relationship to logic and shows how they can extended to first-order rule-based representations. This paper discusses what the representations of uncertainty can bring to the computational logic community and what the computational logic community can bring to those studying reasoning under uncertainty. “It is remarkable that a science which began with the consideration of games of chance should become the most important object of human knowledge...The most important questions of life are, for the most part, really only problems of probability.” “The theory of probabilities is at bottom nothing but common sense reduced to calculus.” — Pierre Simon de Laplace (1794–1827)