Representing Logical Relations Automatically by Probabilistic Logical Dynamical Neural Network

Most of current ANN represents relations in the way of functional approximation. It is good for representing the numeric relations or ratios of things. However, it is not proper to represent logical relations in the form of ratio. Therefore, aiming for representing logical relations directly, we propose a new ANN model PLDNN (Probabilistic Logical Dynamical Neural Network). It defines new neurons and multiple kinds of links (including exciting links and inhibitory links) specified for representing logical relations according to the data. Limited to the perceiving range and other factors, complete information cannot be always gotten. Incomplete information causes the uncertainty and incompletion of logical relations. To deal with it, the probabilities are assigned to the weights of links to indicate the belief degree of logical relations under the uncertain situations. PLDNN creates links on demand to build the network dynamically to represent the logical relations according to the data. It not only uses the weights of links to memorize information, but also uses the network structure to make it store more information. Dynamical network structure makes it high adaptability. The model could be used as the complement to current numeric ANN to deal with logical issues and to expand the application areas of ANN.