To solve any nontrivial problem, it first needs to be conceptualized, taking into account the individual who has the problem. However, a problem is generally associated with more than one individual, as is usually the case in software development. Therefore, this process has to take into account different viewpoints about the problem and any discrepancies that could arise as a result. Traditionally, conceptualization in software engineering has omitted the different viewpoints that the individuals may have of the problem and has inherently enforced consistency in the event of any discrepancies, which are considered as something to be systematically rejected. The paper presents a methodological framework that explicitly drives the conceptualization of different viewpoints and manages the different types of discrepancies that arise between them, which become really important in the process. The definition of this framework is generic, and it is therefore independent of any particular software development paradigm. Its application to software engineering means that viewpoints and their possible discrepancies can be considered in the software process conceptual modeling phase. This application is illustrated by means of what is considered to be a standard problem: the IFIP case.