Domenico Cantone

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

This book presents an intuitive picture-oriented approach to the formative processes technique and to its applications. In the first part the authors introduce basic set-theoretic terminology and properties, the decision problem in set theory, and formative processes. The second part of the book is devoted to applications of the technique of formative processes to decision problems. All chapters contain exercises and the book is appropriate for researchers and graduate students in the area of computer science logic.

This book presents an intuitive picture-oriented approach to the formative processes technique and to its applications. In the first part the authors introduce basic set-theoretic terminology and properties, the decision problem in set theory, and formative processes. The second part of the book is devoted to applications of the technique of formative processes to decision problems. All chapters contain exercises and the book is appropriate for researchers and graduate students in the area of computer science logic.

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.

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.