Symbolic Knowledge Extraction using {\L}ukasiewicz Logics

TL;DR

This paper presents a method that integrates {}ukasiewicz logic with neural networks to facilitate symbolic knowledge extraction and reverse engineering of formulas from data.

Contribution

It introduces a novel approach combining logic and neural networks using {}ukasiewicz logic, enabling easier symbolic rule extraction and translation between symbolic and connectionist models.

Findings

Effective reverse engineering of truth tables

Successful extraction of formulas from real datasets

Maintained learning performance with restricted network plasticity

Abstract

This work describes a methodology that combines logic-based systems and connectionist systems. Our approach uses finite truth-valued {\L}ukasiewicz logic, wherein every connective can be defined by a neuron in an artificial network. This allowed the injection of first-order formulas into a network architecture, and also simplified symbolic rule extraction. For that we trained a neural networks using the Levenderg-Marquardt algorithm, where we restricted the knowledge dissemination in the network structure. This procedure reduces neural network plasticity without drastically damaging the learning performance, thus making the descriptive power of produced neural networks similar to the descriptive power of {\L}ukasiewicz logic language and simplifying the translation between symbolic and connectionist structures. We used this method for reverse engineering truth table and in extraction of formulas from real data sets.