Print on Demand. This book introduces a series of mathematical formulas and techniques for evaluating set theories. These theories, called syllogistic schemes, are applicable to any finite collection of set variables, and easily demonstrate the satisfiability, or truth, of each. It has been shown that any formula can be broken down as a disjunction of syllogistic formulas. The initial part of this book focuses on refining the algorithm outlined above, while the second half explores complexity issues related to classes of set-theoretic formulas. The author proves that if a set of syllogistic schemes is non-empty, then it contains at least one minimum effort scheme, and that in order to check for satisfiability, only such schemes need to be sought. This search, though it involves backtracking, can be piloted quite effectively. This book will be of interest to mathematicians, logicians, and computer scientists. 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.

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Bibliographic Details

Title

The Automation of Syllogistic, Vol. 2: Optimization and Complexity Issues

Publisher

Forgotten Books

Publication Date

2018

Language

English

ISBN 10

1334016011

ISBN 13

9781334016011

Binding

Paperback

Condition

New

Book Type

print-on-demand item

Seller catalogs

Calculus

About this title

Synopsis

Explore how logic and set theory meet computation in this rigorous take on syllogistic schemes and satisfiability.

Delve into methods for deciding when a complex collection of set-theoretic formulas can be true, and learn how these ideas connect to practical complexity results.

This work analyzes a formal system of set-theoretic formulas, introduces notions like p-compatibility and p-compatible DAGs, and shows how satisfiability can be tested by a structured, backtracking-friendly approach. It also covers how certain formula classes relate to well-known complexity results, including NP-completeness, and presents algorithmic perspectives on decision problems for MLSF and its extensions.

How to represent models and equivalence relations that arise from set-theoretic formulas
Techniques for generating and testing candidate schemes that witness satisfiability
Connections between syllogistic reasoning and graph-based decision procedures
NP-completeness results for expanded prenex and simple prenex formula classes

Ideal for readers of mathematical logic, theoretical computer science, and advanced studies in logic and complexity.

"About this title" may belong to another edition of this title.

Store Description

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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Dalton House, 60 Windsor Ave, London, SW19 2RR, United Kingdom

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