I'm writing a MSc thesis right now touching on the subject you're interested in. It's a controversial subject. The author(s) of this paper seems appalled by the mere idea of using formal logic and automatic reasoning and suggests the rule-based approach is hopelessly flawed. Others believe it possible (searching the web for "formal legal reasoning" is an imperfect indicator of the level of interest in the subject) and are investigating different approaches.
I would say that automatic legal reasoning is a much less complex (saying "simpler" would definitely give the wrong idea) problem in European law because it's based on regulations (constitution, laws, international treaties etc.) as opposed to all that plus the entire legal history available to look for precedents, as is characteristic of Anglo-Saxon legal systems. In the latter case, we have to come up with a good way of "understanding" previous cases to be able to identify similarities so a case can be used as a precedent.
Another aspect of the problem is what exactly is the goal. It's much, much harder, for example, to create a system which has to guarantee that the conclusions it draws about a case are of the same quality as those of a good lawyer than it is to create a system which might provide advice or guidance to a lawyer or judge by identifying parts of the law the reasoning engine found to be important for a specific case. This simpler case, basically a decision support system, is what I'm investigating right now.
In my view, the most important aspect of this area of research is that it raises significant philosophical questions about the organization of our societies. For a start, it's obvious you could easily reason automatically about simple/trivial systems, e.g. bike trip rules:
- if we're lost, attempt to match the surroundings to something on the map
- if the trip is long, bring enough food and water
- if we're going into the mountains, we have to carry warmer clothes
...and so on. Now suppose for a minute that encoding laws into formal logic and reasoning automatically is not possible. This can be either because of the way our laws were written (vague programming in a natural language) or because the nature of the emergent life of our society makes it impossible for us to formally describe it using rules. If it's just a matter of existing laws being poorly written, that's solvable. If, on the other hand, society's inner workings can't be formalized in a way which allows automatic reasoning, it sheds completely new light on the legal system, the foundation of any modern country: it becomes clear that the law is fundamentally subjective and any idea of "right" or "wrong" is subject to interpretation, impression etc., reducing the quality of the primary deliverables of law: an absolute sense of justice (the one sold to voters during every political campaign) and dependability and stability of law, which gives people the security to take certain steps (go into a business, invest...whatever) because they expect their actions to be seen in a certain light regardless of the judge or lawyer.
It's a complex, challenging and supremely interesting area of research, one that this handful of sentences only touches on.