1. A Computer Aided Instruction System for the International Law CISG Kaoru Hirota Dept.of Computational Intelligence & Systems Science Tokyo Institute of Technology hirota@hrt.dis.titech.ac.jp

2. “Legal Expert Systems” project 1992-1998 1999-2001 Japanese Ministry of Education, Science and Culture 30 lawyers and computer scientists Hajime YOSHINO （ Meiji Gakuin Univ.) Kaoru HIROTA (Tokyo Institute of Technology) CISG: United Nation Convention on Contracts for the International Sale of Goods Japanese / English versions

3. Background Target Law United Nation Convention on Contract for the International Sale of Goods: CISG Cases Case Law on UNCITL(United Nations Commission on International Trade law) Texts: CLOUT

4. Background Vagueness in Legal Concept CISG Article 14-1 A proposal for concluding a contract addressed to one or more specific persons constitutes an offer if it is sufficiently definite and indicates the intention of the offer to be bound in case of acceptance. A proposal is sufficiently definite if it indicates the goods and expressly or implicitly fixes or makes provision for determining the quantity and the price. Case Based Reasoning

5. Legal Case Based Reasoning ISSUE: α Fuzziness a : Event of Precedent a ' ： Event of Query Case Precedent : A(a) Conclusion: B(a) Query case :A ' (a') If A(a) and A ' are similar: Matching A(a) ≒ A ' (a ' ) The Conclusion of A ' is the same as A’s B ' (a ' ) ≒ B(a)

6. Inference Retrieval CISG Case Base Input Output Overview of Fuzzy Legal Case Based Reasoning System

7. Explanation-based Representation Issue : Vague Legal Concept Feature : The Surface Properties of the Precedent ….. Case Rule : The Deep properties that describe relation between legal judgement and the facts If fact1 is action1 then...

8. Cases Representation (CPF) Case 1: (Issue 1) : (Feature 1) : (Case Rule 1) : (Issue 2) : (Issue n) : Case i: ( ) : Case n: ( ) : case4 : (Malev) ( (issue 41) 14 (1) (No) (feature 41) % It fixes the goods ‘ fix1’(‘fix1_c_n1_1’, [ agt: ‘Malev_proposal’, imp: ‘letter’, obj: ‘engine_system’, ] ). % It fixes the quantity : (case rule 41) % The whole price is not fixed :

9. Similarity in legal Retrieval Logical Product Goods Quantity Proposal Price Weights Average Acceptanc e S(P,Q) Case Feature Similarity Similarity Between Issues Between Cases Precedent Case(P) Query Case(Q) … …

10. Two-stages Fuzzy retrieval Input First stage: First Stage Case Base Second Stages: Second Retrieved Stage Cases in First stage Retrieving the similar case that has the most high similarity degree Retrieving a set of cases that have the same issues Output

11. Similarity of Fuzzy Sets Based on Hausdroff Distance ① d H (A,B,β) = β * (A,B) + (1- β) * (A,B) ② (A,B) = (inf{r;A 0  U (B 0 ; r)} + inf {r; B 0  U(A 0 ; r)} / 2 ③ (A,B) = (inf{r;A 1  U (B 1 ; r)} + inf {r; B 1  U (A 1 ; r)} / 2 µ (v) 1.0 0.0 1.0 v A B

12. Implementation of Fuzzy Legal CBR System Reference Case: Cultivator Precedent Cases Test-Tubes(CLOUT) Screws(CLOUT) Chinchilla pelts(CLOUT) Jet Engine System(CLOUT) Automobile (CLOUT) Shoes(CLOUT) Tire(CLOUT) Electronic(CLOUT)

13. Reference Case: Cultivator Event: proposal The goods are a cultivator. The quantity of the cultivator is one. Concerning the price. The price of the tractor is fixed. The machine contains the tractor and rake Precedent Case: Jet Engine System Event: Proposal The goods are jet engine systems. The quantity of engine systems can be calculated by the quantity of plans that will be purchased. Concerning the price: There is no description about the prices of jet engine systems. The price of Boeing jet engine is fixed. The jet engine system includes a support package, services so on.

14. An Example Reference Case: Cultivator Precedent Case First Stage Second Stage Test-Tubes × -- Screws ○ 0.25 Chinchilla pelts ○ 0.25 Jet Engine System ○ 0.75 Automobile × -- Shoes × -- Tire × -- Electronic × --

17. Selected Publications Journal 1. Kaoru HIROTA, Hajime YOSHINO, MingQiang XU et al: “An Application of Fuzzy Theory to the Case- Based Reasoning of the CISG”,Journal of Advanced Computational Intelligence, Vol.1 No.2 1997, pp.86-93 2. MingQiang XU, Kaoru HIROTA, Hajime YOSHINO: “ A Fuzzy Theoretical Approach to Representation and Inference of Case in CISG”, International Journal of Artificial Intelligence and Law, Vol.7 No.2-3 1999 pp. 259-272 Conference 1. Hajime YOSHINO, MingQiang XU, Kaoru HIROTA: “A Fuzzy Judgement Approach to Inference of Cases in CISG”, The Sixth International Conference on Artificial Intelligence and Law, Poster Proceeding, pp. 60- 64 ， 1997. 6 ， Australia 2. Hajime YOSHINO, MingQiang XU, Kaoru HIROTA: “Representation and Inference of Case with Fuzziness in the CISG”, Proc. of the Fourth International Workshop on a Legal Expert System for the CISG, pp. 5-9, 1997. 6, Australia 3. MingQiang XU, Kaoru HIROTA, Hajime YOSHINO: ”Learning Vague Concepts and Making Argument from Examples by Fuzzy Factors in Interpretive Knowledge-Based System”, The Fifth International Conference on Soft Computing and Information/Intelligence Systems, pp.191-194 ， 1998. 10, Iizuka, Japan