Applied Set Theory And Logic
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Applied Set Theory and Logic
Author: John-Michael Kuczynski
language: en
Publisher: John-Michael Kuczynski
Release Date: 2025-06-12
Applied Set Theory and Logic is a comprehensive guide to the core principles of set theory and mathematical logic, with an emphasis on real-world applications in computer science, engineering, and digital systems. Bridging rigorous theoretical foundations with practical examples, the book explores topics ranging from propositional calculus and predicate logic to modal logic, database systems, circuit verification, and algorithm design. Through hundreds of worked examples and exercises, readers learn to apply logical reasoning to concrete problems in programming, software verification, hardware design, and information systems. Advanced topics include modal logic, recursion, transitivity, Von Neumann and Zermelo ordinals, Boolean algebra, and formal proof techniques. Each chapter highlights the relevance of logic and set theory to contemporary computational systems and digital technologies. Suitable for students, engineers, computer scientists, and researchers, Applied Set Theory and Logic serves both as a theoretical reference and a practical guide to the logical structures that underlie modern technology.
Computational Logic and Set Theory
Author: Jacob T. Schwartz
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-07-16
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.
A Logical Foundation for Potentialist Set Theory
Author: Sharon Berry
language: en
Publisher: Cambridge University Press
Release Date: 2022-02-17
A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.