An algebraic description of XCS
David Pätzel, Jörg Hähner · Proceedings of the Genetic and Evolutionary Computation Conference Companion · 2018
XCS and its derivatives are some of the most prominent Learning Classifier Systems (LCSs). Since XCS's design was done "algorithm first", there existed no formal basis at its inception. Over the past 20 years, several publications analysed parts of the system theoretically but the only approach to a more holistic theory of LCSs in general was never fully adapted. We present an algebraic formalisation of XCS that facilitates formal reasoning about the system and serves as a complement to earlier algorithmic descriptions. Our work is meant to give a fresh impetus to XCS and LCS theory. Since we use the programming language Haskell for our formal expressions we also describe a new abstract XCS framework in the process.