Pattern reasoning: Logical reasoning of neural networks

Abstract

This paper presents pattern reasoning, which is logical reasoning on patterns. Pattern reasoning can be a partial solution to the knowledge acquisition problem. Knowledge acquisition tried to acquire linguistic rules from patterns. On the contrary, we try to modify logics in order to reason with patterns. Patterns are represented as functions, which are approximated by artificial neural networks. Therefore, the logical reasoning of neural networks is studied. Neural networks can be used for inference by a few nonclassical logics because neural networks are multilinear functions (in the discrete domain) and the multilinear function space is the model of a few nonclassical logics such as intermediate logic LC, Lukasiewicz logic, and product logic. Due to space limitations, only intermediate logic LC is briefly explained. © 2001 Scripta Technica, Syst Comp Jpn, 32(2): 1–10, 2001