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Author: Donald W. Loveland
Publisher: Princeton University Press
ISBN: 140084875X
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
Author: Donald W. Loveland
Publisher: Princeton University Press
ISBN: 140084875X
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses
Author: Donald W. Loveland
Publisher:
ISBN: 9781400898763
Category :
Languages : en
Pages : 338
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Book Description
Three Views of Logic: Mathematics, Philosophy, and Computer ScienceDonald W. Loveland, Richard E. Hodel & S.G. SterrettCloth | January 2014 | 49.50 / £34.95 | ISBN: 9780691160443344 pp. | 7 x 10 | 7 line illus. 10 tables. Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into.
Author: Zondervan,
Publisher: Zondervan Academic
ISBN: 0310873983
Category : Religion
Languages : en
Pages : 486
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Book Description
For Christians, the issues raised by the different views on creation and evolution are challenging. Can a "young earth" be reconciled with a universe that appears to be billions of years old? Does scientific evidence point to a God who designed the universe and life in all its complexity? Three Views on Creation and Evolution deals with these and similar concerns as it looks at three dominant schools of Christian thought. Proponents of young earth creationism, old earth creationism, and theistic evolution each present their different views, tell why the controversy is important, and describe the interplay between their understandings of science and theology. Each view is critiqued by various scholars, and the entire discussion is summarized by Phillip E. Johnson and Richard H. Bube. The Counterpoints series provides a forum for comparison and critique of different views on issues important to Christians. Counterpoints books address two categories: Church Life and Bible and Theology. Complete your library with other books in the Counterpoints series.
Author: Steve Wilkens
Publisher: InterVarsity Press
ISBN: 0830840400
Category : Religion
Languages : en
Pages : 190
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Book Description
Steve Wilkens edits a debate between three different understandings of the relationship between faith and reason, between theology and philosophy. The three views include: Faith and Philosophy in Tension, Faith Seeking Understanding and the Thomistic Synthesis. This introduction to a timeless quandary is an essential resource for students.
Author: Richard E. Hodel
Publisher: Courier Corporation
ISBN: 0486497852
Category : Mathematics
Languages : en
Pages : 514
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Book Description
This comprehensive overview ofmathematical logic is designedprimarily for advanced undergraduatesand graduate studentsof mathematics. The treatmentalso contains much of interest toadvanced students in computerscience and philosophy. Topics include propositional logic;first-order languages and logic; incompleteness, undecidability,and indefinability; recursive functions; computability;and Hilbert’s Tenth Problem.Reprint of the PWS Publishing Company, Boston, 1995edition.
Author: David J. Pym
Publisher: Springer Science & Business Media
ISBN: 9401700915
Category : Mathematics
Languages : en
Pages : 323
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Book Description
This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
Author: Peter B. Andrews
Publisher: Springer Science & Business Media
ISBN: 9401599343
Category : Mathematics
Languages : en
Pages : 404
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Book Description
In case you are considering to adopt this book for courses with over 50 students, please contact
[email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.
Author: Hao Wang
Publisher: Courier Corporation
ISBN: 0486171043
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.
Author: Robert R. Stoll
Publisher: Courier Corporation
ISBN: 0486139646
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author: Robert L. Thomas
Publisher: Kregel Academic
ISBN: 9780825498824
Category : Religion
Languages : en
Pages : 404
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Book Description
Noted evangelical scholars present the best contemporary insights into the three dominant views on the origins of the Synoptic Gospels.
