Designing arithmetic neural primitive for sub-symbolic aggregation of linguistic assessments

Abstract

The very first step towards a challenging goal of creation of monolithic generic neuro-symbolic systems is application of sub-symbolic ideas to particular symbolic algorithms like aggregation of fuzzy linguistic assessments during Linguistic Decision Making. A novel theoretical idea is to express this aggregation as structural manipulations and translate them in a neuroalgorithm. Tensor Product Representation (TPR) methodology provides a generic framework of designing neural networks that do not require training and produce an exact result equivalent to the result of symbolic algorithms. This paper demonstrates design of TPR-based arithmetic as a basic building block for expressing linguistic assessments aggregation on a sub-symbolic level and a neural architecture for the basic arithmetic operation.