Domenico Cantone

Eugenio Omodeo

Alfredo Ferro

The authors describe computational techniques for deciding formulae in set theory. The eventual aim of such a work is to automate simple proofs over a wide range of mathematical areas. This volume reports on a successful series of investigations in one of the most important sub-domains:elementary set theory.

Computable Set Theory

Pietro Ursino

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.

An Introduction to the Technique of Formative Processes in Set Theory

Jacob T. Schwartz

Eugenio G. Omodeo

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.

Applying Formalized Logic to Analysis

Computational Logic and Set Theory

Alberto Policriti

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.

Domenico Cantone

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