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

TL;DR

This paper introduces Multi-entity Bayesian networks (MEBN), a formal system combining first-order logic with Bayesian probability, enabling reasoning about complex, uncertain relational domains in intelligent systems.

Contribution

MEBN extends Bayesian networks to incorporate first-order logic, allowing representation of probabilistic models over complex relational structures.

Findings

MEBN can model probability distributions over first-order theories.

The system is demonstrated with an example inspired by Star Trek.

MEBN bridges the gap between logic and probabilistic reasoning.

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. 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.