Mathematical Sciences: Universal Algebra and Lattice Theory

这项研究的长期目标是提供由布尔代数和附加运算组成的各种代数结构的统一处理。将在这一框架内作出重大努力，制定一种对计算程序和相关概念的解释，比动态代数的概念更能真实地代表这些概念的运算特性。这将导致关于布尔代数上各种类型的算子的其他普遍感兴趣的问题。这项研究涉及逻辑、代数和计算机科学的广泛领域。普适代数和格子的主题将从它们本身以及它们在理论计算机科学中的应用来研究。

The long range goal of this research is to provide a unified treatment of various algebraic structures consisting of a Boolean algebra with additional operations. A major effort will be made to develop within that framework an interpretation of computing programs and of related concepts that represents more faithfully the operational properties of these concepts than does the notion of a dynamic algebra. This will lead to other questions of general interest concerning various classes of operators on a Boolean algebra. This research is at the broad interface of logic, algebra and computer science. The subject of universal algebra and lattices will be studied for their own right and for their applications to theoretical computer science.