In legal case-based reasoning (CBR), there exist problems concerning fuzziness, e.g., representation of precedents, their retrieval, and similarity measures. In our proposed fuzzy legal CBR system, the issues and features of precedent are characterized on the basis of the facts of precedent and statute rule. The case rule that is used for interpreting the court judgment, which cannot be obtained from the statute rule directly, is made by experts. Fuzziness is represented by membership functions. Features and case rules, written in terms of Compound Predicate Formula (CPF) and frame, are stored in a case base. Cases similar to a new case are retrieved by issues and features, and an inference is made by case rules. A user interface is devised for this system. The system proposed here will be used for law education, where the target law of the system is contract, especially as it relates to the United Nations Convention on Contracts for the International Sale of Goods (CISG).
The previous theory of pure polymer fluid is extended to polymer solutions. The partition function and the complete thermodynamic description for polymer solutions on a lattice model are obtained. With neglecting of the influence of preferential interaction on configuration, the free energy of Flory-Huggins is recovered. The temperature-independent portion of effective interaction parameter is explained from the molecular origins, and the observed composition dependence of is provided on a molecular basis. The values calculated from the present theory match the experimental spinodals data. However, the mean field approximation has an important effect not only on spinodals and binodals, but also on the interaction parameter.
A definition concerning the spanning sub graph and spanning sub graph circle is given. Use the enumerating methods of spanning sub circle; seek out the spanning sub graph of spanning trees. The theorems of constructing and enumerating the spanning trees are proved. The methods of enumerating and constructing connected graph spanning tree are proposed. The application examples of construction theorem and enumerating theorem are given. the spanning sub graphs number of five plane graph and the construction of Constituent sub-graph are introduced, thus verifying constructing and enumerating theorem are useful and effective. This method Is a Simple and easy method to construct the spanning tree of connected graph.
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