Merging Connectionism and Logicism in Knowledge Representation

There are two main schools in knowledge representation: Connectionism and Logicism.As two independent formalisms, they are often put separately in knowledge representation.While Logicism expresses in symbolic formulas, Connectionism expresses in graphs or networks.The purpose of this paper is to investigate that it is possible we can merge the two formalisms, Connectionism and Logicism, into one formalism?Firstly, in this paper I will introduce Logicism representations.Examples are proposition logic, first order predicate logic, second order predicate logic.Next, I will introduce Connectionism.Examples of Connectionism are directed graph, semantic network, artificial neural network.And lastly, I will try to merge the two formalisms into one formalism according to three mathematical theorems.