  Intelligent systems in an open world must reason about many interacting
entities related to each other in diverse ways and having uncertain features
and relationships. Traditional probabilistic languages lack the expressive
power to handle relational domains. Classical first-order logic is sufficiently
expressive, but lacks a coherent plausible reasoning capability. Recent years
have seen the emergence of a variety of approaches to integrating first-order
logic, probability, and machine learning. This paper presents Multi-entity
Bayesian networks (MEBN), a formal system that integrates First Order Logic
(FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks
to allow representation of graphical models with repeated sub-structures, and
can express a probability distribution over models of any consistent, finitely
axiomatizable first-order theory. We present the logic using an example
inspired by the Paramount Series StarTrek.
