Introduction to Mathematics of Satisfiability / Edition 1

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $86.54
Usually ships in 1-2 business days
(Save 17%)
Other sellers (Hardcover)
  • All (1) from $86.54   
  • New (1) from $86.54   
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any coupons and promotions
Seller since 2007

Feedback rating:



New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.


Ships from: Avenel, NJ

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Sort by


Although this area has a history of over 80 years, it was not until the creation of efficient SAT solvers in the mid-1990s that it became practically important, finding applications in electronic design automation, hardware and software verification, combinatorial optimization, and more. Exploring the theoretical and practical aspects of satisfiability, Introduction to Mathematics of Satisfiability focuses on the satisfiability of theories consisting of propositional logic formulas. It describes how SAT solvers and techniques are applied to problems in mathematics and computer science as well as important applications in computer engineering.

The book first deals with logic fundamentals, including the syntax of propositional logic, complete sets of functors, normal forms, the Craig lemma, and compactness. It then examines clauses, their proof theory and semantics, and basic complexity issues of propositional logic. The final chapters on knowledge representation cover finite runs of Turing machines and encodings into SAT. One of the pioneers of answer set programming, the author shows how constraint satisfaction systems can be worked out by satisfiability solvers and how answer set programming can be used for knowledge representation.

Read More Show Less

Editorial Reviews

From the Publisher
This interesting book covers the satisfiability problem with a strong focus on its mathematical background. It includes the famous theorems on the problem as well as some exotic results. … To improve understanding, the book offers plenty of insightful examples, elegant proofs, and each chapter ends with about a dozen exercises. … What I like most about the book is the wide variety of ideas of which the usefulness to solve many problems is almost tangible … the book covers more potentially powerful techniques, such as the cutting plane rule and various autarky detection methods, than those used in the latest state-of-the-art solvers. … apart from the collection of elegant proofs — from major theorems to exotic lemmas — Introduction to Mathematics of Satisfiability is also a source of inspiration for students and researchers in the field of satisfiability.
Theory and Practice of Logic Programming, Vol. 11, Issue 1

… Through very current material at the heart of the book, the author presents and analyzes general algorithms that work better than exhaustive search … Marek also covers important special cases of the problem that turn out vulnerable to clever special attacks. … Summing Up: Recommended.
CHOICE, September 2010

… an invaluable reference for anyone who is interested in issues ranging from theoretical mathematical logic to computational logic. The book maintains a nice tradeoff between formalism and clarity. … The author excels at relating his expositions to the current state of the art, and he recognizes when his discussions are only the tip of the iceberg. … its most significant contribution is its accessible explanations of how and why algorithms and ideas expose work.
—Carlos Linares Lopez, Computing Reviews, March 2010

Read More Show Less

Product Details

Meet the Author

Victor W. Marek is a professor in the Department of Computer Science at the University of Kentucky.

Read More Show Less

Table of Contents


Sets, Lattices, and Boolean Algebras

Sets and Set-Theoretic Notation

Posets, Lattices, and Boolean Algebras

Well-Orderings and Ordinals

The Fixpoint Theorem

Introduction to Propositional Logic

Syntax of Propositional Logic

Semantics of Propositional Logic


Tautologies and Substitutions

Lindenbaum Algebra



Semantical Consequence

Normal Forms

Canonical Negation-Normal Form

Occurrences of Variables and Three-Valued Logic

Canonical Forms

Reduced Normal Forms

Complete Normal Forms

Lindenbaum Algebra Revisited

Other Normal Forms

The Craig Lemma

Craig Lemma

Strong Craig Lemma

Tying up Loose Ends

Complete Sets of Functors

Beyond De Morgan Functors


Field Structure in Bool

Incomplete Sets of Functors, Post Classes

Post Criterion for Completeness

If-Then-Else Functor

Compactness Theorem

König Lemma

Compactness, Denumerable Case

Continuity of the Operator Cn

Clausal Logic and Resolution

Clausal Logic

Resolution Rule

Completeness Theorem

Query Answering with Resolution

Davis–Putnam Lemma

Semantic Resolution

Autark and Lean Sets

Algorithms for SAT

Table Method

Hintikka Sets


Davis–Putnam Algorithm

Boolean Constraint Propagation

The DPLL Algorithm

Improvements to DPLL?

Reduction of the Search SAT to Decision SAT

Easy Cases of SAT

Positive and Negative Formulas

Horn Formulas

Autarkies for Horn Theories

Dual Horn Formulas

Krom Formulas and 2-SAT

Renameable Classes of Formulas

XOR Formulas

SAT, Integer Programming, and Matrix Algebra

Encoding of SAT as Inequalities

Resolution and Other Rules of Proof

Pigeon-Hole Principle and the Cutting Plane Rule

Satisfiability and {-1, 1}-Integer Programming

Embedding SAT into Matrix Algebra

Coding Runs of Turing Machine, and "Mix-and-Match"

Turing Machines

The Language

Coding the Runs

Correctness of Our Coding

Reduction to 3-Clauses

Coding Formulas as Clauses and Circuits

Decision Problem for Autarkies

Search Problem for Autarkies

Either-Or CNFs

Other Cases

Computational Knowledge Representation with SAT

Encoding into SAT, DIMACS Format

Knowledge Representation over Finite Domains

Cardinality Constraints, the Language Lcc

Weight Constraints

Monotone Constraints

Knowledge Representation and Constraint Satisfaction

Extensional Relations, CWA

Constraint Satisfaction and SAT

Satisfiability as Constraint Satisfaction

Polynomial Cases of Boolean CSP

Schaefer Dichotomy Theorem

Answer Set Programming

Horn Logic Revisited

Models of Programs

Supported Models

Stable Models

Answer Set Programming and SAT

Knowledge Representation and ASP

Complexity Issues for ASP




Exercises appear at the end of each chapter.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)