Decision Procedures for Elementary Sublanguages of Set Theory: X. Multilevel Syllogistic Extended by the Singleton and Powerset Operators (Classic Reprint) - Hardcover

D. Cantone

Hardcover

ISBN 10: 0656050411 ISBN 13: 9780656050413

Publisher: Forgotten Books, 2018

Synopsis

Understand a new decision procedure for a rich class of set-theoretic formulas.

This work shows that the satisfiability problem remains solvable when extending multilevel syllogistic with singleton and powerset operators.

Written for researchers and students in logic and theoretical computer science, the text frames how a carefully designed procedure combines syntactic and model-theoretic ideas to decide formulas built from union, intersection, set difference, powerset, and singleton, using standard set-theoretic predicates and boolean connectives. It explains the intended interpretation and proves that satisfiable formulas have boundable models, leading to a concrete decidability result.

The paper surveys the progression from well-known decidability results to a decision procedure for a broader language, and outlines the key constructs that enable the proof. It emphasizes how canonical models and a nondeterministic standardization algorithm work together to test satisfiability.

• The language MLSSP and its injective satisfiability reduction to a simpler subtheory.
• The construction of places, P-nodes, and a staged algorithm that ensures correct modeling of clauses.
• The Main Inductive Lemma and its role in establishing partial correctness of the procedure.
• Culminating corollaries, including the decidability of the MLSSP class and model-size bounds.

Ideal for readers of formal logic and advanced set theory who want a rigorous, computational take on satisfiability in set-theoretic languages.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0656050411
• ISBN 13: 9780656050413
• Binding: Hardcover
• Number of pages: 59