Decision Procedures for Elementary Sublanguages of Set Theory: XI
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.32
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Add to basketItem description from seller
Print on Demand. This book extends the decision procedures for set theory previously developed by the author for quantied and unquantied languages. This eleventh volume of the series builds upon prior work by examining set operators, set predicates, cardinality operators, cardinality predicates and function operators within elementary Boolean connectives. It presents a finite and uniform procedure that decides whether a given formula possesses a model or not, reducing the problem to the satisability problem for conjunctions of atoms. By way of disjunctive normal form, it is demonstrated that constructs like set difference or the Singleton predicate are equisatisfiable to conjunctions of positive atoms. The author demonstrates the satisability problem for three-sorted language, which properly extends the purely set-theoretical part of the theory considered in previous volumes, exhibiting a finite and uniform procedure that is capable of deciding whether a given formula has a model. The book concludes by considering D, INV, SINGLEVALUED, PAIRIN as operators, discussing their satisability conditions, and arguing that the class of formulas in the language of the book has a solvable satisability problem. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781333042547_0
- Title
- Decision Procedures for Elementary Sublanguages of Set Theory: XI
- Author
- D. Cantone, J. T. Schwartz
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 133304254X
- ISBN 13
- 9781333042547
- Seller catalogs
- Calculus
The text presents a rigorous construction that models conjuncts and clauses, explains injectivity of representations, and develops a procedure to verify satisfiability. Readers will see how abstract definitions translate into procedural steps, with proofs that establish closure properties and representational correctness. The approach blends formal logic with constructive techniques, offering a precise path from syntax to models.
- How to build injective representations that satisfy a given conjunction of clauses.
- Techniques for proving that a model respects all conjuncts, including value and edge relations.
- Formal lemmas and corollaries that connect representations to the underlying graph structures.
- A decision-procedure framework for a broad class of set-theoretic expressions.
Ideal for researchers and advanced students in logic, set theory, and automated deduction who want to understand how to extend syllogistic reasoning with new operators while keeping decision procedures feasible.
"Synopsis" may belong to another edition of this title.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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