This observation that "legal logic" is not quite the same as traditional rational-thought logic has led to an interesting "legal reasoning" subfield of AI over the past decade or so (with some precursors dating back further) that tries to formalize exactly what logic it is following, and how it differs from traditional rationality. That area develops alternative logics, reasoning procedures, etc., in order to do things like simulate case outcomes, suggest possible arguments to make, evaluate alternative strategies, etc. Until relatively recently many people did think that the right way to make a legal reasoning system was to treat the law as logical rules, and the legal reasoning problem as a problem of rational inference over rules+evidence... which turns out not to be that accurate an account of how law actually operates.