Decision Procedures for Elementary Sublanguages of Set Theory: XI

D. Cantone, J. T. Schwartz

ISBN 10: 133304254X / ISBN 13: 9781333042547

Verlag: Forgotten Books, 2018

Beschreibung

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.

Bestandsnummer des Verkäufers 9781333042547_0

Bibliografische Details

• Titel: Decision Procedures for Elementary Sublanguages of Set Theory: XI
• Verlag: Forgotten Books
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 133304254X
• ISBN-13: 9781333042547
• Einband: Paperback
• Zustand: New
• Buchtyp: print-on-demand item
• Verkäuferkataloge:
  • Calculus

Über diesen Titel

Inhaltsangabe

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.

Reseña del editor

Excerpt from Decision Procedures for Elementary Sublanguages of Set Theory: XI. Multilevel Syllogistic Extended by Some Elementary Map Constructs

This paper tackles the satisfiability problem for the one-sorted language E, which properly extends the purely set-theoretical part (i.e. With no cardinality constructs) of the theory considered in [fos]. In particular we will exhibit a finite and uniform procedure which decides for any given formula P of E whether P has a model or not.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.