| Closure Spaces and Logic 1996 Edition Contributor(s): Martin, N. M. (Author), Pollard, S. (Author) |
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ISBN: 0792341104 ISBN-13: 9780792341109 Publisher: Springer OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: July 1996 Annotation: The book exmaines closure spaces, an abstract mathematical theory, with special emphasis on results applicable to formal logic. The theory is developed, conceptually and methodologically, as part of topology. At the least, the book shows how techniques and results from topology can be usefully employed in the theory of deductive systems. At most, since it shows that much of logical theory can be represented within closure space theory, the abstract theory of derivability and consequence can be considered a branch of applied topology. One upshot of this appears to be that the concepts of logic need not be overtly linguistic nor do logical systems need to have the syntax they are usually assumed to have. Audience: The book presupposes very little technical knowledge, but can probably be read most easily by someone with a background in symbolic logic or, even better, upper division or graduate mathematics. It should be of interest to logicians and, to a lesser degree, computer scientists and other mathematicians. |
| Additional Information |
| BISAC Categories: - Mathematics | Logic - Mathematics | Geometry - General - Philosophy | Logic |
| Dewey: 514.32 |
| LCCN: 96018772 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.63" H x 6.14" W x 9.21" (1.17 lbs) 230 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 generalization has an extreme advantage in connection with application to logic, since the most important closure notion in logic, deductive closure, in most cases does not generate a V-space, since the closure of the null set typically consists of the "logical truths" of the logic being examined. |