Lattice Computing: A Mathematical Modelling Paradigm for Cyber-Physical System Applications – Mathematics 2022, 10(2), 271

By “model”, we mean a mathematical description of a world aspect [1]. Mathematical models, implemented in software, are often engaged to drive hardware.

Models are typically developed in the Euclidean space R^N, for an integer number N, where R is the totally ordered lattice of real numbers. Note that modelling in R^N is inherently related to the physical world, where the conventional measurement process gives rise to the set, R, of real numbers. Nevertheless, alternative spaces for modelling, even in physics, have been proposed, such as a probability space whose “event space” suggests a mathematical lattice. The interest here is in explicit, rigorous modelling in a mathematical lattice data domain. Mathematical lattices emerged in the mid-19th century as a spin-off of work on the formalizing of propositional logic [1]. Furthermore, it was Birkhoff’s work in the mid-1930s [2] that started the general development of mathematical lattice theory.