Empirical Logic for Bio-Inspired Soft Computing: Illustrative Applications in Control Engineering and Cluster Analysis

Empirical logic (EL) is a bio-inspired soft computing approach to rule-based decision-making that emphasizes intuitive, experience-based reasoning. While its theoretical foundations have been established in previous work, its practical applicability and accessibility have so far received less attention. This paper addresses this gap by providing two representative application examples from distinct domains: control engineering and cluster analysis. The first example demonstrates the use of EL for the speed control of a DC drive, highlighting its ability to achieve competitive dynamic performance with a small number of intuitive rules. The second example introduces a novel approach to cluster analysis, where cluster structures emerge from the collective interaction of EL rules rather than from the optimization of a predefined objective function. In addition, the paper emphasizes the availability of publicly accessible software realizations of EL, including a Maple-based prototype and a Python framework, which enable direct experimentation and practical use. By combining illustrative applications with executable tools, the paper aims to facilitate the transition from conceptual understanding to practical deployment and to support further exploration of EL in applied soft computing contexts.