First-Order Bayesian Logic

Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical first-order logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a built-in, semantically grounded capability for reasoning under uncertainty renders classical first-order logic inadequate for many important classes of problems. General-purpose languages are beginning to emerge for which the fundamental logical basis is probability. Increasingly expressive probabilistic languages demand a theoretical foundation that fully integrates classical first-order logic and probability. In first-order Bayesian logic (FOBL), probability distributions are defined over interpretations of classical first-order axiom systems. Predicates and functions of a classical first-order theory correspond to a random variables in the corresponding first-order Bayesian theory. This is a natural correspondence, given that random variables are formalized in mathematical statistics as measurable functions on a probability space. A formal system called Multi-Entity Bayesian Networks (MEBN) is presented for composing distributions on interpretations by instantiating and combining parameterized fragments of directed graphical models. A construction is given of a MEBN theory that assigns a non-zer