Narrow Results

A modularity concept for structuring and developing large logic programs and logical knowledge bases is presented. The concept is motivated from work in the field of algebraic specification, and enforces an extreme modularity discipline that goes beyond the one found in imperative or logic programming languages. As concrete programming languages (respectively knowledge representation formalisms), we consider Horn logic and equational logic programming. We give formal semantics for single modules and discuss correctness and verification issues. Large systems are constructed as interconnections of single modules. We introduce the so-called module operations of composition, actualization, and union, and give results concerning compositionality of semantics and correctness preservation.

In applying the boundary element method to an acoustic interior problem modeled as a single domain, even a small change of the cavity geometry affects the whole system matrix. Thus, calculating sensitivities for each intermediate shape is performed independently during iterations for an optimum shape. By utilizing the sub-domain modularization capability of the MBEM, however, the matrix inversion task is performed only once for the initial shape during whole iterations. This can reduce the total computational costs of finding an optimum shape design and the computational efficiency increases as the number of iterations increases. A demonstration example is given by a two-dimensional automotive interior cavity.

We characterize rings over which every cotorsion module is pure injective (Xu rings) in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known for the special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts.