形式化描述领域特定建模语言的结构语义

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"本文主要探讨了领域特定建模语言(DSML)和元建模语言(DSMML)的结构语义的正式表示方法。针对DSML和DSMML的非正式定义导致其结构语义无法严格描述以及基于此的属性无法系统分析和验证的问题,文章提出了一种形式化的描述方法。首先,通过代数理论给出了领域和元领域的正式定义,其次,建立了从领域和元领域到相应一阶逻辑系统的映射机制,以实现结构语义的精确表达和分析。" 在软件工程中,领域特定建模语言(DSML)是一种用于特定领域系统设计和建模的定制化语言。它允许专家以接近领域概念的方式进行建模,提高了效率和准确性。然而,DSML的非正式定义是当前面临的一个挑战,这使得语言的结构语义难以被准确理解和验证。同样,元建模语言(DSMML)用于定义DSML的语法和语义,其非正式性同样阻碍了对DSML的深入理解和使用。 该研究论文提出了一个创新的解决方案,即采用形式化的方法来描述DSML和DSMML的结构语义。首先,通过代数理论建立了一个基础,对领域和元领域进行了形式化的定义。这种方法有助于清晰地界定各个领域的边界和特征,确保了语言的基础框架具有严谨性和一致性。 接下来,论文引入了一种映射机制,将领域和元领域的概念映射到一阶逻辑系统。一阶逻辑是一种强大的数学工具,常用于形式化表述和推理。这种映射机制使得DSML和DSMML的结构语义可以被转化为可计算的形式,从而能够进行精确的分析和验证。这意味着模型的正确性和一致性可以被系统地检查,避免了潜在的错误和漏洞。 通过这样的形式化处理,开发者和分析人员能够更有效地理解、验证和改进DSML和DSMML。这种方法的实施对于提升DSML的标准化和可靠性,以及推动领域特定建模在实际应用中的发展具有重要意义。此外,它也为后续的工具开发和自动化验证提供了坚实的理论基础。 总结来说,这篇论文的工作是对DSML和DSMML结构语义形式化表示的探索,旨在解决由于非正式定义带来的问题,提高建模语言的精确度和可分析性,为软件建模领域带来了重要的理论贡献。

For macroscopically anisotropic media in which the variations in the phase stiffness tensor are small, formal solutions to the boundary-value problem have been developed in the form of perturbation series (Dederichs and Zeller, 1973; Gubernatis and Krumhansl, 1975 ; Willis, 1981). Due to the nature of the integral operator, one must contend with conditionally convergent integrals. One approach to this problem is to carry out a “renormalization” procedure which amounts to identifying physically what the conditionally convergent terms ought to contribute and replacing them by convergent terms that make this contribution (McCoy, 1979). For the special case of macroscopically isotropic media, the first few terms of this perturbation expansion have been explicitly given in terms of certain statistical correlation functions for both three-dimensional media (Beran and Molyneux, 1966 ; Milton and Phan-Thien, 1982) and two-dimensional media (Silnutzer, 1972 ; Milton, 1982). A drawback of all of these classical perturbation expansions is that they are only valid for media in which the moduli of the phases are nearly the same, albeit applicable for arbitrary volume fractions. In this paper we develop new, exact perturbation expansions for the effective stiffness tensor of macroscopically anisotropic composite media consisting of two isotropic phases by introducing an integral equation for the so-called “cavity” strain field. The expansions are not formal but rather the nth-order tensor coefficients are given explicitly in terms of integrals over products of certain tensor fields and a determinant involving n-point statistical correlation functions that render the integrals absolutely convergent in the infinite-volume limit. Thus, no renormalization analysis is required because the procedure used to solve the integral equation systematically leads to absolutely convergent integrals. Another useful feature of the expansions is that they converge rapidly for a class of dispersions for all volume fractions, even when the phase moduli differ significantly.

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