Sinossi
This text examines 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. It shows how techniques and results from topology can be usefully employed in the theory of deductive systems, and 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. The text presupposes very little technical knowledge, but is more suited to someone with a background in symbolic logic or upper division or graduate mathematics. It should be of interest to logicians and computer scientists.
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Contenuti
Preface. 1. Logic and Topology. 2. Basic Topological Properties. 3. Some Theorems of Tarski. 4. Continuous Functions. 5. Homeomorphisms. 6. Closed Bases and Closure: Semantics I. 7. Theory of Complete Lattices. 8. Closed Bases and Closure: Semantics II. 9. Truth Functions. Bibliography. Index.
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Book by Jackson Martin Pollard S
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Closure Spaces and Logic [= Mathematics and Its Applications; Volume 369]
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Dordrecht - Boston - London: Kluwer Academic Publishers 1996, 1996
ISBN 10: 0792341104
ISBN 13: 9780792341109
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Closure Spaces and Logic (Mathematics and Its Applications, 369)
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Closure Spaces and Logic
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 252 pp. Englisch. Codice articolo 9780792341109
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 . Codice articolo 5967815
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Closure Spaces and Logic
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Condizione: Gut. Zustand: Gut | Sprache: Englisch | Produktart: Bücher | 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. Codice articolo 2223846/203
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Condizione: Hervorragend. Zustand: Hervorragend | Sprache: Englisch | Produktart: Bücher | 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. Codice articolo 2223846/1
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Closure Spaces and Logic
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Springer, Springer Jul 1996, 1996
ISBN 10: 0792341104
ISBN 13: 9780792341109
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 252 pp. Englisch. Codice articolo 9780792341109
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