Understanding how people exchange beliefs giving rise to complex attitude-identity systems is crucial for the social sciences, data science, and policymaking. Yet, many established research methods struggle to account for the ecological complexity of these processes, especially with regard to the structural architecture of attitude systems, their embedding in identity, and the challenges of comparing empirical results. ResIN (Response Item Networks), an innovative method inspired by Belief Network Analysis (BNA), seeks to address many of the limitations of traditional analytical approaches. However, its lack of grounding in a formal theory of measurement has thus far constrained its interpretability, particularly when comparing results across multiple datasets. In this chapter, we address this limitation by introducing a theoretical framework of belief networks inspired by ResIN. This framework, which we refer to as Belief Network Theory (BNT), aims to balance information complexity and research practicality. BNT is particularly well-suited for advanced research scenarios, such as comparing complex attitude-identity systems across diverse data types or assessing changes within these systems over time. By grounding belief networks in a formal theory of measurement, BNT offers a principled, flexible, and data-compatible tool for studying how belief systems evolve, interconnect, and shape social reality.