The Mathematics of the Models of Reference is a detailed exposition of the modeling of physical and informational reality pursued by iLabs Milan ( www.ilabs.it ), a private research lab in applied Artificial Intelligence. Based on an original approach to cellular automata theory, this book includes an array of axiomatic formal theories, ranging from a discrete, mereological model of the structure of space-time, to non-standard computation and recursion theory. The appendices to the volume explain the applications of the theory in the algorithmic recapture of a variety of physical, biological, and cognitive phenomena. Francesco Berto Logic & Formal Modeling @ iLabs PhD in Philosophy, has studied at the University of Notre Dame (Indiana, USA), at the Sorbonne-Ecole Normale Superieure of Paris, and is currently lecturer at the University of Aberdeen. He has published various papers and monographs in ontology and the philosophy of logic. Gabriele Rossi Director of iLabs A.I. Department @ iLabs Has a degree in Economic and Social Disciplines at the Bocconi University in Milan and is CEO of Diagramma, a leading company in insurance software applications. Expert in Artificial Intelligence, in 2007 he has co-authored with Antonella Canonico the book Semi-Immortality, a manifesto of European transhumanism. Jacopo Tagliabue Chief Scientist for Qualitative Modeling @ iLabs A PhD student with a degree in Philosophy at the University San Raffaele of Milan, has studied Economics at LSE, Statistics at New York University, and Complex Systems at the Santa Fe Institute. He has published papers in ontology and non-standard computation.