Computational Logic and Set Theory
Title | Computational Logic and Set Theory PDF eBook |
Author | Jacob T. Schwartz |
Publisher | Springer Science & Business Media |
Pages | 426 |
Release | 2011-07-16 |
Genre | Computers |
ISBN | 0857298089 |
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.
Set Theory for Computing
Title | Set Theory for Computing PDF eBook |
Author | Domenico Cantone |
Publisher | Springer Science & Business Media |
Pages | 440 |
Release | 2001-06-26 |
Genre | Computers |
ISBN | 9780387951973 |
"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.
Sets, Logic and Maths for Computing
Title | Sets, Logic and Maths for Computing PDF eBook |
Author | David Makinson |
Publisher | Springer Science & Business Media |
Pages | 302 |
Release | 2012-02-27 |
Genre | Computers |
ISBN | 1447125002 |
This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduates need to study computing. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. Features: teaches finite math as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear confusions; provides numerous exercises, with selected solutions.
A Computational Logic
Title | A Computational Logic PDF eBook |
Author | Robert S. Boyer |
Publisher | Academic Press |
Pages | 414 |
Release | 2014-06-25 |
Genre | Mathematics |
ISBN | 1483277887 |
ACM Monograph Series: A Computational Logic focuses on the use of induction in proving theorems, including the use of lemmas and axioms, free variables, equalities, and generalization. The publication first elaborates on a sketch of the theory and two simple examples, a precise definition of the theory, and correctness of a tautology-checker. Topics include mechanical proofs, informal development, formal specification of the problem, well-founded relations, natural numbers, and literal atoms. The book then examines the use of type information to simplify formulas, use of axioms and lemmas as rewrite rules, and the use of definitions. Topics include nonrecursive functions, computing values, free variables in hypothesis, infinite backwards chaining, infinite looping, computing type sets, and type prescriptions. The manuscript takes a look at rewriting terms and simplifying clauses, eliminating destructors and irrelevance, using equalities, and generalization. Concerns include reasons for eliminating isolated hypotheses, precise statement of the generalization heuristic, restricting generalizations, precise use of equalities, and multiple destructors and infinite looping. The publication is a vital source of data for researchers interested in computational logic.
Sets, Logic, Computation
Title | Sets, Logic, Computation PDF eBook |
Author | Richard Zach |
Publisher | |
Pages | 418 |
Release | 2021-07-13 |
Genre | |
ISBN |
A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.
Concise Introduction to Logic and Set Theory
Title | Concise Introduction to Logic and Set Theory PDF eBook |
Author | Iqbal H. Jebril |
Publisher | CRC Press |
Pages | 171 |
Release | 2021-09-30 |
Genre | Mathematics |
ISBN | 0429665989 |
This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.
Sets, Logic and Categories
Title | Sets, Logic and Categories PDF eBook |
Author | Peter J. Cameron |
Publisher | Springer Science & Business Media |
Pages | 191 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1447105893 |
Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.