Decision Procedures for Elementary Sublanguages of Set Theory; Vi
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.40
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book delves into the realm of understanding and resolving a particular undeclared theory of sets, specifically concerning the language involving empty sets, equality, membership, union, set differences, and powersets. The theory the author explores has been previously examined but with the powerset operator omitted, while this book builds on that work by including it. Using techniques and ideas developed in the author's previous works, this text presents an algorithm that reveals whether any formula within this theory is satisfiable. Throughout the book, the author proves that the conditions presented are both necessary and sufficient for this satisfiability, marking an important contribution to the field. 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 # 9781332887477_0
- Title
- Decision Procedures for Elementary Sublanguages of Set Theory; Vi
- Author
- D. Cantone, A. Ferro
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332887473
- ISBN 13
- 9781332887477
- Seller catalogs
- Geometry
Decidability for a targeted set theory language with powerset
Explore a focused method for deciding whether complex statements in an elementary sublanguage of set theory can be satisfied. This edition develops an algorithmic approach to determine satisfiability of conjunctions that include membership, equality, and powerset constraints, all built from a compact collection of clause types. It also presents a detailed set of conditions that must hold for a model to exist, along with constructive steps to build such a model when possible.
The text walks through the main result: a complete set of necessary and sufficient conditions for satisfiability, including a precise list of finite structures and relationships that must be arranged among variables and places. It then shows how these conditions lead to a decision procedure and outlines how to bound the rank of models in terms of the input size. The work combines formal definitions, lemmas, and a nondeterministic initialization algorithm to connect syntactic constraints with semantic possibilities, ensuring the problem is algorithmically decidable.- Learn how to model the satisfiability problem with places, nodes, and edges that reflect powerset behavior.
- See how a finite, stepwise initialization procedure helps build a valid interpretation.
- Understand the six conditions (C1–C6) that characterize satisfiable clause sets.
- Discover how to bound the rank of potential models based on the input size.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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