Decision Procedures for Elementary Sublanguages of Set Theory: XI

D. Cantone, J. T. Schwartz

ISBN 10: 133304254X / ISBN 13: 9781333042547

Published by Forgotten Books, 2018

About this Item

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

Bibliographic Details

• Title: Decision Procedures for Elementary Sublanguages of Set Theory: XI
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 133304254X
• ISBN 13: 9781333042547
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

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.