Propositional Knowledge Representation and Reasoning in Restricted Boltzmann Machines

TL;DR

This paper introduces a novel, less complex method for representing propositional logic in restricted Boltzmann machines, enabling better reasoning capabilities in connectionist networks, with promising real-world dataset results.

Contribution

It proposes a new approach to encode propositional formulas in RBMs, improving reasoning over traditional neural network methods and addressing previous complexity issues.

Findings

Effective encoding of propositional formulas in RBMs

Improved reasoning capabilities demonstrated on real datasets

Simpler approach for logical implications and Horn clauses

Abstract

While knowledge representation and reasoning are considered the keys for human-level artificial intelligence, connectionist networks have been shown successful in a broad range of applications due to their capacity for robust learning and flexible inference under uncertainty. The idea of representing symbolic knowledge in connectionist networks has been well-received and attracted much attention from research community as this can establish a foundation for integration of scalable learning and sound reasoning. In previous work, there exist a number of approaches that map logical inference rules with feed-forward propagation of artificial neural networks (ANN). However, the discriminative structure of an ANN requires the separation of input/output variables which makes it difficult for general reasoning where any variables should be inferable. Other approaches address this issue by employing generative models such as symmetric connectionist networks, however, they are difficult and convoluted. In this paper we propose a novel method to represent propositional formulas in restricted Boltzmann machines which is less complex, especially in the cases of logical implications and Horn clauses. An integration system is then developed and evaluated in real datasets which shows promising results.