This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. This new edition includes material on AE calculus, Herbrand's theorem, Gentzen's theorem, and related topics.
This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. This new edition includes material on AE calculus, Herbrand's theorem, Gentzen's theorem, and related topics.
Über den Autor
Melvin Fitting was a student of Raymond Smullyan. His dissertation became his first book, Intuitionistic Logic, Model Theory, and Forcing (1969). Since then he has authored or co-authored eleven books and served as editor for another three, as well as writing over 130 papers and book chapters. Among the areas he has worked in are intensional logic, semantics for logic programming, fixpoint theories of truth, and justification logic. A significant part of his work has involved developing tableau systems for non-classical logics, thus generalizing the classical systems of his mentor Smullyan. In 2012 he received the Herbrand Award from the Conference on Automated Deduction, largely for this tableau work, and in 2019 he received an honorary PhD from the University of Bucharest. He was on the faculty of the City University of New York from 1969 to his retirement in 2013. At CUNY he was at the undergraduate Lehman College, and at the City University Graduate Center, where he was in the Departments of Mathematics, Computer Science, and Philosophy. He is now an emeritus Professor, but very much active.
Richard L. Mendelsohn studied philosophy, logic and linguistics while a graduate student at M.I.T. Among the areas he has worked in are modal logic, philosophical logic, philosophy of language, history of early modern analytic philosophy, and the philosophy of Gottlob Frege. He has authored or coauthored 3 books, and many articles and reviews. He was on the faculty of the City University of New York from 1968 until his retirement in 2014. He continues now as an emeritus Professor at CUNY. In addition, after visiting for many years, he has, since 2014, been an Adjunct Professor of Logic and the Philosophy of Science at the University of California, Irvine and a member of the Center for the Advancement of Logic there. At CUNY he taught at the undergraduate Lehman College and at the City University Graduate Center, where he was a member of the Department of Philosophy, serving as chair from 1993 to 1998, as well as a member of the Department of Linguistics.
Zusammenfassung
This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. This new edition includes material on AE calculus, Herbrand's theorem, Gentzen's theorem, and related topics.
Inhaltsverzeichnis
1 Background.- 2 Propositional Logic.- 2.1 Introduction.- 2.2 Propositional Logic-Syntax.- 2.3 Propositional Logic-Semantics.- 2.4 Boolean Valuations.- 2.5 The Replacement Theorem.- 2.6 Uniform Notation.- 2.7 König's Lemma.- 2.8 Normal Forms.- 2.9 Normal Form Implementations.- 3 Semantic Tableaux and Resolution.- 3.1 Propositional Semantic Tableaux.- 3.2 Propositional Tableaux Implementations.- 3.3 Propositional Resolution.- 3.4 Soundness.- 3.5 Hintikka's Lemma.- 3.6 The Model Existence Theorem.- 3.7 Tableau and Resolution Completeness.- 3.8 Completeness With Restrictions.- 3.9 Propositional Consequence.- 4 Other Propositional Proof Procedures.- 4.1 Hilbert Systems.- 4.2 Natural Deduction.- 4.3 The Sequent Calculus.- 4.4 The Davis-Putnam Procedure.- 4.5 Computational Complexity.- 5 First-Order Logic.- 5.1 First-Order Logic-Syntax.- 5.2 Substitutions.- 5.3 First-Order Semantics.- 5.4 Herbrand Models.- 5.5 First-Order Uniform Notation.- 5.6 Hintikka's Lemma.- 5.7 Parameters.- 5.8 The Model Existence Theorem.- 5.9 Applications.- 5.10 Logical Consequence.- 6 First-Order Proof Procedures.- 6.1 First-Order Semantic Tableaux.- 6.2 First-Order Resolution.- 6.3 Soundness.- 6.4 Completeness.- 6.5 Hilbert Systems.- 6.6 Natural Deduction and Gentzen Sequents.- 7 Implementing Tableaux and Resolution.- 7.1 What Next.- 7.2 Unification.- 7.3 Unification Implemented.- 7.4 Free-Variable Semantic Tableaux.- 7.5 A Tableau Implementation.- 7.6 Free-Variable Resolution.- 7.7 Soundness.- 7.8 Free-Variable Tableau Completeness.- 7.9 Free-Variable Resolution Completeness.- 8 Further First-Order Features.- 8.1 Introduction.- 8.2 The Replacement Theorem.- 8.3 Skolemization.- 8.4 Prenex Form.- 8.5 The AE-Calculus.- 8.6 Herbrand's Theorem.- 8.7 Herbrand's Theorem, Constructively.-8.8 Gentzen's Theorem.- 8.9 Cut Elimination.- 8.10 Do Cuts Shorten Proofs?.- 8.11 Craig's Interpolation Theorem.- 8.12 Craig's Interpolation Theorem-Constructively.- 8.13 Beth's Definability Theorem.- 8.14 Lyndon's Homomorphism Theorem.- 9 Equality.- 9.1 Introduction.- 9.2 Syntax and Semantics.- 9.3 The Equality Axioms.- 9.4 Hintikka's Lemma.- 9.5 The Model Existence Theorem.- 9.6 Consequences.- 9.7 Tableau and Resolution Systems.- 9.8 Alternate Tableau and Resolution Systems.- 9.9 A Free-Variable Tableau System With Equality.- 9.10 A Tableau Implementation With Equality.- 9.11 Paramodulation.- References.
