We present the results of our research that is positioned in the domain of system modeling. In particular, we present an object-oriented paradigm that provides a logically rigorous and complete theoretical base for various existing object-oriented frameworks. The strong points of the paradigm are presented by demonstrating how the paradigm can resolve a number of existing problems of the Unified Modeling Language (UML). The analysis of these problems and the proposed paradigm-based solutions represent an original research approach towards software systems modeling; the research approach that is based on the theories like Russells theory of types and Tarskis declarative semantics. The paper advances the current state of research in software systems modeling frameworks in general and the state of UML research in particular.