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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.
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 AEtnaNova 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.
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" provides a comprehensive account of set-oriented symbolic manipulation methods suitable for automated reasoning. Its main objective is twofold: 1) to provide a flexible formalization for a variety of set languages, and 2) to clarify the semantics of set constructs firmly established in modern specification languages and in the programming practice. Topics include: semantic unification, decision algorithms, modal logics, declarative programming, tableau-based proof techniques, and theory-based theorem proving. The style of presentation is self-contained, rigorous and accurate. Some familiarity with symbolic logic is helpful but not a requirement. This book is a useful resource for all advanced students, professionals, and researchers in computing sciences, artificial intelligence, automated reasoning, logic, and computational mathematics. It will serve to complement their intuitive understanding of set concepts with the ability to master them by symbolic and logically based algorithmic methods and deductive techniques.
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 AEtnaNova 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."
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