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Decision Procedures for Elementary Sublanguages of Set Theory: X. Multilevel Syllogistic Extended by the Singleton and Powerset Operators (Classic Reprint) - Softcover
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.
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Decision Procedures for Elementary Sublanguages of Set Theory: X
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Paperback. Condition: New. Print on Demand. This book explores the intersection of set theory and propositional logic, focusing on the satisfiability problem and relationships to model theory. The author, a respected figure in mathematical logic, provides an in-depth analysis of the class of formulae involving set-theoretic atoms, Boolean operators, equality, and membership predicates. The book delves into decision procedures for these formulae, establishing solvable satisfiability problems for a specific class within this wider group. Moreover, it demonstrates a fundamental connection between satisfiability and the existence of hereditarily finite models for these formulae, providing novel insights into the interplay between syntax and model theory. Through detailed proofs and technical exposition, this book offers a significant contribution to the study of set theory and its applications in propositional logic and model theory. 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. print-on-demand item. Seller Inventory # 9781333072308_0
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Decision Procedures for Elementary Sublanguages of Set Theory X Multilevel Syllogistic Extended by the Singleton and Powerset Operators Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333072308
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Decision Procedures for Elementary Sublanguages of Set Theory X Multilevel Syllogistic Extended by the Singleton and Powerset Operators Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333072308
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