Set Theory for Computing

An up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. This book is of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

Set Theory for Computing offers an up-to-date and comprehensive account of set-oriented symbolic manipulation and automated reasoning methods. Mastering today's variety of systems with crisp, formal tools is a prerequisite for a high degree of control over sets and aggregates. The many algorithmic methods and deductive techniques in this book offer readers a clear view of the use of set-theoretic notions in such critical areas as specification of problems, data types, and solution methods; algorithmic program verification; and automated deduction.
The rigorous and largely self-contained style of presentation addresses readers wanting to complement their set intuition with the ability to exploit it in specification and verification and master it by symbolic, logically based techniques and methods. This book will be of interest to graduates and researchers in theoretical computer science and computational logic and automated reasoning.

From the reviews:

"The book is an up-to-date and well-organized collection of techniques and results concerning the problem of dealing with sets in computer science. In particular, the book can be very interesting for postgraduate students and researchers in computer science and logic. The book is largely self-contained and the style of presentation is extremely rigorous and accurate. ... this will become a sort of classic work for automated deduction and declarative programming and surely it deserves to find a place in all scientific libraries." (A. Dovier, Theory and Practise of Logic Programming, Vol. 3 (1), 2003)

"Set theory has played the role of a lingua franca for modern mathematics. The authors of this monograph intend to extend this service to computer science, artificial intelligence, and computational mathematics. Several variants of ZF, which are meant for different applications, are surveyed and concrete, computable models are investigated. There is an extensive list of references, an index of symbols and an index of terms." (J.M. Plotkin, Zentralblatt MATH, Vol. 981, 2002)

Autorentext

Domenico Cantone is a professor at the Università di Catania. He has been a visiting professor at New York University, Stanford University, ICSI (Berkeley), and Karlsruhe. His interests include mathematical and computer science logic, in particular set theory. Pietro Ursino is a lecturer at the Università dell'Insubria, his interests include mathematical logic.

Inhalt
1 What Is Computable Set Theory?.- 2 Logical Background.- 3 Axiomatic Views of Aggregates.- 4 Semantic Views of Aggregates.- 5 Sets for Problem Solving.- 6 Decision Problems and Some Solutions.- 7 Inference Techniques and Methods.- 8 Set/Hyperset Unification Algorithms.- 9 (*) A Syllogistic Solitaire.- 10 Stratified Syllogistics.- 11 Quantitative Set Reasoning.- 12 Set Theory for Nonclassic Logics.- 13 Logic Programming with Sets.- 14 Syllogistic Tableaux.- References.- Tables and Index of Symbols.- Association and priority rules.- Truth tables.- Common abbreviations in first-order languages.- Substitution-related notation.- Map-related notation.- Function-related notation.- Basic laws on sets.- Abbreviations in mathematical English.- Index of Terms.