Of Starships and Klingons: Bayesian Logic for the 23rd Century

Abstract

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, whereas 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. We present the logic using an example inspired by the Paramount Series Star Trek. MEBN semantics integrates random variables as formalized in mathematical statistics with model theoretic semantics for first-order logic.