I am working on a project whose object language is in non-monotonic logic. Since the project involves reasoning about the models, I am thinking of translating a non-monotonic problem into a first-order logic, use model theory in first-order monotone logic to solve the problem, then translate the results back to a non-monotonic logic. However, this seems cumbersome.
Could you please provide me with a book or paper reference on model theory in non-monotonic logics. Preferably, classical topics such as Compactness theorem, Incompleteness theorems and Stable theories should be included.