Formal Semantics of Model Fields in Annotation-based Specifications

It is widely recognized that abstraction and modularization are indispensable for specification of real-world programs. In source-code level program specification and verification, model fields are a common means for those goals. However, it remains a challenge to provide a well-founded formal semantics for the general case in which the abstraction relation defining a model field is non-functional.
In this paper, we discuss and compare several possibilities for defining model field semantics, and we give a complete formal semantics for the general case. Our analysis and the proposed semantics is based on a generalization of Hilbert's epsilon terms.