The Logic Structure Behind Mathematical Models：An Axiomatic Framework for System Dynamics

Modeling complex systems typically involves multiscale analysis, multiphysics coupling, and cross-domain integration. However, existing methodologies predominantly focus on constructing and solving specific equations, lacking a unified, explicit expression for underlying logical structures, which limits model comparison and combination. To address this issue, this paper proposes Axiomatic System Dynamics (ASD), a formal modeling language that decouples a model's logical structure from its mathematical form by formalizing a mathematical model as a combination of a conceptual model and its mathematical realization. Grounded in primitive concepts—state, action, and parameter—ASD introduces generalized constitutive relationships to formulate a unified representation of system evolution. On this basis, a modular "conceptual model first, mathematical model second" paradigm is established to explicitly characterize causal relationships and identify logical isomorphisms across varied mathematical models. Through case studies spanning Newtonian mechanics, ideal gases, material constitutive relationships, and soil consolidation theory, we demonstrate that classical cross-domain theories can be formalized as specific implementations of their respective underlying system dynamics "mother structure." Ultimately, ASD provides a meta-modeling framework independent of concrete mathematical forms, establishing a methodological foundation for logical expression, model comparison, and the meso-level deductive synthesis of cross-domain theories.