On neural-logic networks

Abstract

The paper consists of two parts. The first part describes a class of networks called inference networks. An inference network is a directed graph with 'primitive', 'OR', 'AND' and 'NOT' nodes. 'Primitive' nodes can be given with any truth values from which the truth values of all other nodes can be calculated step by step through the paths. Inference networks can be used to model all kinds of logics. In the second part of the paper, another class of networks called neural-logic networks is introduced. A neural-logic network is also a directed graph whose nodes also represent logical statements and whose edges also represent logical links of these statements. However the nodes are not classified as OR nodes, AND nodes or NOT nodes. The truth-value of each node is an ordered pair (x, y) where x and y are non-negative real numbers with 0≤x+y≤1. The number x indicates the 'amount' of evidence that the statement is true while the value of y indicates the 'amount' of evidence that the statement is false. A neural-logic network is basically a neural network. However, it behaves very much like a logical system and yet contains all the features of an inference network.