Before revision:  Based on previous work, here we define declarative modeling of complex biological systems by defining the  semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects , we define semantics-preserving implementation and semantics-approximating model reduction transformations , and we outline a "meta-hierarchy" URLanizing declarative models and the mathematical methods that can fruitfully manipulate them.
After revision:  Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects , we define semantics-preserving implementation and semantics-approximating model reduction transformations , and we outline a "meta-hierarchy" URLanizing declarative models and the mathematical methods that can fruitfully manipulate them.