A Computational Logic

A Computational Logic
Author :
Publisher : Academic Press
Total Pages : 414
Release :
ISBN-10 : 9781483277882
ISBN-13 : 1483277887
Rating : 4/5 (82 Downloads)

Synopsis A Computational Logic by : Robert S. Boyer

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.

A Computational Logic Handbook

A Computational Logic Handbook
Author :
Publisher : Elsevier
Total Pages : 427
Release :
ISBN-10 : 9781483277783
ISBN-13 : 148327778X
Rating : 4/5 (83 Downloads)

Synopsis A Computational Logic Handbook by : Robert S. Boyer

Perspectives in Computing: A Computational Logic Handbook contains a precise description of the logic and a detailed reference guide to the associated mechanical theorem proving system, including a primer for the logic as a functional programming language, an introduction to proofs in the logic, and a primer for the mechanical theorem. The publication first offers information on a primer for the logic, formalization within the logic, and a precise description of the logic. Discussions focus on induction and recursion, quantification, explicit value terms, dealing with features and omissions, elementary mathematical relationships, Boolean operators, and conventional data structures. The text then takes a look at proving theorems in the logic, mechanized proofs in the logic, and an introduction to the system. The text examines the processes involved in using the theorem prover, four classes of rules generated from lemmas, and aborting or interrupting commands. Topics include executable counterparts, toggle, elimination of irrelevancy, heuristic use of equalities, representation of formulas, type sets, and the crucial check points in a proof attempt. The publication is a vital reference for researchers interested in computational logic.

Computational Logic and Human Thinking

Computational Logic and Human Thinking
Author :
Publisher :
Total Pages : 310
Release :
ISBN-10 : 1107214459
ISBN-13 : 9781107214453
Rating : 4/5 (59 Downloads)

Synopsis Computational Logic and Human Thinking by : Robert Kowalski

"The practical benefits of computational logic need not be limited to mathematics and computing. As this book shows, ordinary people in their everyday lives can profit from the recent advances that have been developed for artificial intelligence. The book draws upon related developments in various fields from philosophy to psychology and law. It pays special attention to the integration of logic with decision theory, and the use of logic to improve the clarity and coherence of communication in natural languages such as English. This book is essential reading for teachers and researchers who may be out of touch with the latest developments in computational logic. It will also be useful in any undergraduate course that teaches practical thinking, problem solving or communication skills. Its informal presentation makes the book accessible to readers from any background, but optional, more formal, chapters are also included for those who are more technically oriented"--

Logical Foundations of Mathematics and Computational Complexity

Logical Foundations of Mathematics and Computational Complexity
Author :
Publisher : Springer Science & Business Media
Total Pages : 699
Release :
ISBN-10 : 9783319001197
ISBN-13 : 3319001191
Rating : 4/5 (97 Downloads)

Synopsis Logical Foundations of Mathematics and Computational Complexity by : Pavel Pudlák

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.

Handbook of Mathematics and Computational Science

Handbook of Mathematics and Computational Science
Author :
Publisher : Springer Science & Business Media
Total Pages : 1064
Release :
ISBN-10 : 0387947469
ISBN-13 : 9780387947464
Rating : 4/5 (69 Downloads)

Synopsis Handbook of Mathematics and Computational Science by : John W. Harris

This book gathers thousands of up-to-date equations, formulas, tables, illustrations, and explanations into one invaluable volume. It includes over a thousand pages of mathematical material as well as chapters on probability, mathematical statistics, fuzzy logic, and neural networks. It also contains computer language overviews of C, Fortran, and Pascal.

Fundamentals of Logic and Computation

Fundamentals of Logic and Computation
Author :
Publisher : Springer Nature
Total Pages : 225
Release :
ISBN-10 : 9783030878825
ISBN-13 : 3030878821
Rating : 4/5 (25 Downloads)

Synopsis Fundamentals of Logic and Computation by : Zhe Hou

This textbook aims to help the reader develop an in-depth understanding of logical reasoning and gain knowledge of the theory of computation. The book combines theoretical teaching and practical exercises; the latter is realised in Isabelle/HOL, a modern theorem prover, and PAT, an industry-scale model checker. I also give entry-level tutorials on the two software to help the reader get started. By the end of the book, the reader should be proficient in both software. Content-wise, this book focuses on the syntax, semantics and proof theory of various logics; automata theory, formal languages, computability and complexity. The final chapter closes the gap with a discussion on the insight that links logic with computation. This book is written for a high-level undergraduate course or a Master's course. The hybrid skill set of practical theorem proving and model checking should be helpful for the future of readers should they pursue a research career or engineering in formal methods.

Handbook of Computational Social Choice

Handbook of Computational Social Choice
Author :
Publisher : Cambridge University Press
Total Pages : 553
Release :
ISBN-10 : 9781316489758
ISBN-13 : 1316489752
Rating : 4/5 (58 Downloads)

Synopsis Handbook of Computational Social Choice by : Felix Brandt

The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book.

Mathematical Aspects of Logic Programming Semantics

Mathematical Aspects of Logic Programming Semantics
Author :
Publisher : CRC Press
Total Pages : 307
Release :
ISBN-10 : 9781000218725
ISBN-13 : 1000218724
Rating : 4/5 (25 Downloads)

Synopsis Mathematical Aspects of Logic Programming Semantics by : Pascal Hitzler

Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.

Logic for Computer Science

Logic for Computer Science
Author :
Publisher : Courier Dover Publications
Total Pages : 532
Release :
ISBN-10 : 9780486780825
ISBN-13 : 0486780821
Rating : 4/5 (25 Downloads)

Synopsis Logic for Computer Science by : Jean H. Gallier

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

Computational Intelligence In Manufacturing Handbook

Computational Intelligence In Manufacturing Handbook
Author :
Publisher : CRC Press
Total Pages : 573
Release :
ISBN-10 : 9781420041934
ISBN-13 : 1420041932
Rating : 4/5 (34 Downloads)

Synopsis Computational Intelligence In Manufacturing Handbook by : Jun Wang

Despite the large volume of publications devoted to neural networks, fuzzy logic, and evolutionary programming, few address the applications of computational intelligence in design and manufacturing. Computational Intelligence in Manufacturing Handbook fills this void as it covers the most recent advances in this area and state-of-the-art applicati