I dont think the law can be modeled as a logically consistent set of rules, because there are so many laws that its always possible to apply correct deductive arguments to arrive at different "correct" conclusions which contradict each other.

A much better model is to view the legal system as a tool used by the rich and powerful to exert their domination over the oppressed classes. This has historically always been what the law was for, going back all the way to ancient Rome. This is also what makes the concept of a "rule of law, not of man" such a revolutionary concept.