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Full Description
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.
Contents
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.
