Legal systems typically use non-monotonic logic. Most formal logic systems, particularly in mathematical fields, use monotonic logic. Monotonic logic isn't well suited for the law or most other areas of human activity.

If you want an entire legal system formally defined in logic, you're going to have to do a ton of novel work in expanding the understanding of and application of non-monotonic logic because there isn't much scholarship compared to monotonic logic systems.

That said, France is one of the only countries that has tried anything like this. Their tax system is required to be defined and expressed algorithmically, and they even built a programming language and compiler tool chain to do this. I think it uses monotonic logic, though, and I don't think anybody has seriously suggested the French tax code is something to be copied, neither as a tax code nor an approach to legal codification more generally.