Mathematical Sciences: Universal Algebra and Lattice Theory

本研究的长远目标是提供一种统一处理由布尔代数和附加运算组成的各种代数结构的方法。一个主要的努力将是在这个框架内发展对计算程序和相关概念的解释，它比动态代数的概念更忠实地代表这些概念的操作特性。这将导致关于布尔代数上各种算子类的其他普遍感兴趣的问题。这项研究是在广泛的接口逻辑，代数和计算机科学。通用代数和格的主题将被研究为它们自己的权利和它们在理论计算机科学中的应用。

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.