The paper presents two approaches to model System-of-Systems on lative logic point of view. Lative logic is a general framework to construct building blocks of logic using Category Theory as its metalanguage. This approach reveals avenues to describe System of -Systems themselves, and to model information and processes they posers, using some reasonable modelling languages in a computational manner, thus, touching foundations of computational science. After presenting some preliminary notes, the paper explains the main steps to construct lative logics, and then give two approaches to System-of-System modelling. Finally, the paper presents a survey to some applications.