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Automated Reasoning in Higher-order Logic: Set Comprehension and Extensionality in Church's Type Theory (Studies in Logic, Logic and Cognitive Systems) [Paperback]

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Item description for Automated Reasoning in Higher-order Logic: Set Comprehension and Extensionality in Church's Type Theory (Studies in Logic, Logic and Cognitive Systems) by Chad E. Brown...

Many mathematical and computational concepts can be represented in a natural way using higher-order logic. Consequently, higher-order logic has become an important topic of research. /Automated Reasoning in Higher-Order Logic/ presents both a theoretical analysis of fragments of higher-order logic as well as a complete automated search procedure for an extensional form of higher-order logic. The first part of the book provides a detailed presentation of the theory (syntax and semantics) of fragments of higher-order logic. The fragments differ in the amount of extensionality and set comprehension principles included. Three families of sequent calculi are defined and proven sound and complete with respect to appropriate model classes. Using the model constructions in the book, different versions of Cantor's theorem are determined to not be provable in certain fragments. In fact, some versions of Cantor's theorem are independent of other versions (in sufficiently weak fragments). In the second part of the book, an automated proof procedure for extensional type theory is described. Proving completeness of such a higher-order search procedure is a nontrivial task. The book provides such a completeness proof by first proving completeness of the ground case and then proving appropriate lifting results. /Automated Reasoning in Higher-Order Logic/ is an essential document for researchers in higher-order logic and higher-order theorem proving. The book is also essential reading for programmers implementing or extending higher-order search procedures. Users of higher-order theorem provers can use the book to improve their understanding of the underlying logical systems.



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Item Specifications...


Pages   542
Est. Packaging Dimensions:   Length: 1.25" Width: 6.5" Height: 9.5"
Weight:   1.76 lbs.
Binding  Softcover
Release Date   Oct 22, 2007
Publisher   College Publications
ISBN  1904987575  
ISBN13  9781904987574  


Availability  0 units.


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1Books > Special Features > New & Used Textbooks > Computer Science & Information Systems > Artificial Intelligence
2Books > Subjects > Computers & Internet > Computer Science > Artificial Intelligence > Computer Mathematics
3Books > Subjects > Computers & Internet > Computer Science > Artificial Intelligence > General
4Books > Subjects > Computers & Internet > Computer Science > Artificial Intelligence > Theory of Computing
5Books > Subjects > Computers & Internet > General
6Books > Subjects > Computers & Internet > Programming > Algorithms > Fuzzy Logic
7Books > Subjects > Nonfiction > Philosophy > Logic & Language
8Books > Subjects > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Logic
9Books > Subjects > Science > Mathematics > General
10Books > Subjects > Science > Mathematics > Pure Mathematics > Logic



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