Personalized systems are a response to the increasing number of resources on the Internet. In order to facilitate their design and creation, we aim at formalizing them. In this paper, we consider the relationship between a personalized application and its non-personalized counterpart. We argue that a personalized application is a formal extension of a non-personalized one. We aim at characterizing the syntactic differences between the expression of the personalized and non-personalized versions of the application. Situation calculus is our framework to formalize applications. We introduce two scenarios of non-personalized application that we personalize to illustrate our approach.