Title: Decision Procedures for Elementary Sublanguages of Set Theory XI Multilevel Syllogistic Extended by Some Elementary Map Constructs Classic Reprint
Publisher: LULU PR
Publication Date: 2018
Language: English
ISBN 10: 133304254X
ISBN 13: 9781333042547
Binding: PAP
Condition: New
Weight: 118 grams

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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.

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