A01=Donald W. Loveland
A01=Richard Hodel
A01=S. G. Sterrett
A01=Susan Sterrett
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Algorithm
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Author_Donald W. Loveland
Author_Richard Hodel
Author_S. G. Sterrett
Author_Susan Sterrett
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Characterization (mathematics)
Church-Turing thesis
Classical logic
Computability
Computability theory
Computable function
Computation
Conjunction elimination
Conjunction introduction
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Decidability (logic)
Decision problem
Deduction theorem
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Deontic logic
Diagram (category theory)
Disjunctive syllogism
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Existential quantification
First-order logic
Formal proof
Four-valued logic
Inference
Intuitionistic logic
Language_English
Logic
Logic programming
Logical conjunction
Logical connective
Logical consequence
Logical disjunction
Material implication (rule of inference)
Mathematical induction
Mathematical logic
Mathematical proof
Modal logic
Natural deduction
Negation
Negation introduction
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Paraconsistent logic
Partially ordered set
Philosophical logic
Philosophy of mathematics
Predicate (mathematical logic)
Predicate logic
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Primitive recursive function
Proof calculus
Proof procedure
Proof theory
Propositional calculus
Propositional variable
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Quantifier (logic)
Reasoning system
Recursion (computer science)
Recursive set
Register machine
Relevance logic
Resolution (logic)
Rule of inference
Semantics
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Substructural logic
Tautology (logic)
Theorem
Truth table
Truth value
Turing machine
Turing's proof
Variable (computer science)
Word problem (mathematics)
Product details
- ISBN 9780691160443
- Weight: 680g
- Dimensions: 178 x 254mm
- Publication Date: 26 Jan 2014
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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
Donald W. Loveland is professor emeritus of computer science at Duke University and the author of Automated Theorem Proving: A Logical Basis. Richard E. Hodel is associate professor emeritus of mathematics at Duke University and the author of An Introduction to Mathematical Logic. S. G. Sterrett is the Curtis D. Gridley Distinguished Professor of History and Philosophy of Science at Wichita State University and the author of Wittgenstein Flies a Kite: A Story of Models of Wings and Models of the World.
