Algebra And Logic

Architecture, Applications and Foundation

"Embark on a comprehensive exploration of the foundational principles and practical applications of logic and computer design with this essential textbook. 'Logic and Computer Design Fundamentals: From Theory to Practice' provides a comprehensive introduction to the core concepts that underpin modern digital systems.

This book examines an abstract mathematical theory, placing special emphasis on results applicable to formal logic. If a theory is especially abstract, it may find a natural home within several of the more familiar branches of mathematics. This is the case with the theory of closure spaces. It might be considered part of topology, lattice theory, universal algebra or, no doubt, one of several other branches of mathematics as well. In our development we have treated it, conceptually and methodologically, as part of topology, partly because we first thought ofthe basic structure involved (closure space), as a generalization of Frechet's concept V-space. V-spaces have been used in some developments of general topology as a generalization of topological space. Indeed, when in the early '50s, one of us started thinking about closure spaces, we thought ofit as the generalization of Frechet V­ space which comes from not requiring the null set to be CLOSURE SPACES ANDLOGIC XlI closed(as it is in V-spaces).

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come.