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.
Author(s): Domenico Cantone, Eugenio Omodeo, Alberto Policriti
Series: Monographs in Computer Science
Publisher: Springer
Year: 2001
Language: English
Pages: 419
Tags: Mathematics of Computing; Mathematical Logic and Formal Languages
Front Matter....Pages i-xviii
Front Matter....Pages 1-1
What Is Computable Set Theory?....Pages 3-13
Logical Background....Pages 14-58
Front Matter....Pages 59-59
Axiomatic Views of Aggregates....Pages 61-86
Semantic Views of Aggregates....Pages 87-111
Sets for Problem Solving....Pages 112-147
Decision Problems and Some Solutions....Pages 148-195
Inference Techniques and Methods....Pages 196-244
Front Matter....Pages 245-245
Set/Hyperset Unification Algorithms....Pages 247-264
(*) A Syllogistic Solitaire....Pages 265-283
Stratified Syllogistics....Pages 284-303
Front Matter....Pages 305-305
Quantitative Set Reasoning....Pages 307-317
Set Theory for Nonclassic Logics....Pages 318-339
Logic Programming with Sets....Pages 340-349
Syllogistic Tableaux....Pages 350-373
Back Matter....Pages 374-409
