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In the domain of law, various real situations are expressed as relations and/or combinations of legal knowledge items (legal concepts, articles of law, etc). Such knowledge items (legal facts, events) cannot be precisely defined. Legal judgement is performed based on resemblance of legal knowledge and facts. In our system, vague legal knowledge is saved in the fuzzy relational database, and legal inference is realized as fuzzy inference. The target law for this system is the United Nations Convention on Contracts for the International Sale of Goods (CISG).

Knowledge representation and similarity measure play an important role in classifying vague legal concepts. In order to consider fuzziness and context-sensitive effects, for the representation of the precedent, a fuzzy factor hierarchy is studied. Current distance-based and feature-based similarity measures are only surface level ones that can't make more than a comparison between objects. Therefore, a deep level similarity measure that can evaluate the results of the surface level one is needed. A structural similarity: factor-based similarity, that is integrated by the surface level and deep level ones is proposed. An argument model that is based on the proposed knowledge representation and similarity measure is proposed. Considering the vague legal concept in the United Nations Convention on Contracts for the International Sale of Goods(CISG), a fuzzy legal argument system is constructed. The main purpose of the proposed system is to support the law education.