A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

Development of a New Assessment System to Evaluate Students' English Communicative Capacities in China

The purpose of this study was to develop a new English assessment system to evaluate Chinese students' English communicative capacities. Since there is more interaction with people from English-speaking countries, Chinese people attach more importance to English oral skills, and a lot of Western English teaching methods were introduced into China to improve students' English communicative capacities. However, traditional paper-written examinations, like the English test of higher education entry examination, cannot evaluate it effectively. This study explored the perceptions of two Chinese English-language teachers and two Chinese students about English assessment system. A qualitative research method using telephone interviews was conducted in this study. The findings showed that the most possible ways to assess Chinese students' English communicative capacities were paper-written examination and person-machine conversations, although measures should be taken to improve these two models. On the other hand, the model of person-person conversation was the ideal assessment tool but was hard to achieve at the current stage.