Set Theory for Computing: From Decision Procedures to Declarative Programming With Sets

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)