Logic for computer science: foundations of automatic theorem proving
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 i...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Mineola, New York
Dover Publications, Inc.
2015
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| Edition: | Second edition, Dover edition |
| Series: | Dover books on computer science
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| Subjects: | |
| Online Access: | TUM01 |
| Summary: | 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 fir |
| Item Description: | "This Dover edition, first published in 2015, is an unabridged republication of the revised 2003 online edition of the work originally published by Harper & Row, New York, in 1986. A new Preface to the Dover Edition has been specially prepared for this volume." |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9780486805085 0486805085 |
Staff View
MARC
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| 245 | 1 | 0 | |a Logic for computer science |b foundations of automatic theorem proving |c Jean H. Gallier, Department of Computer and Information Science University of Pennsylvania |
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| 505 | 8 | |a Cover; Title page; Copyright; Table of Contents; Preface (Dover Edition); Preface (1985 Edition); How to use this Book as A Text; Chapter 1: Introduction; Chapter 2: Mathematical Preliminaries; 2.1 Relations, Functions, Partial Orders, Induction; 2.1.1 Relations; 2.1.2 Partial Functions, Total Functions; 2.1.3 Composition of Relations and Functions; 2.1.4 Injections, Surjections, Bijections; 2.1.5 Direct Image, Inverse Image; 2.1.6 Sequences; 2.1.7 Natural Numbers and Countability; 2.1.8 Equivalence Relations; 2.1.9 Partial and Total Orders; 2.1.10 Well-Founded Sets and Complete Induction | |
| 505 | 8 | |a 3.3.1 The Semantics of Propositions3.3.2 Satisfiability, Unsatisfiability, Tautologies; 3.3.3 Truth Functions and Functionally Complete Sets of Connectives; 3.3.4 Logical Equivalence and Boolean Algebras; * 3.3.5 NP-Complete Problems; Problems; 3.4 Proof Theory of Propositional Logic: The Gentzen System G2 3.4.1 Basic Idea: Searching for a Counter Example; 3.4.2 Sequents and the Gentzen System G'; 3.4.3 Falsifiable and Valid Sequents; 3.4.4 Axioms, Deduction Trees, Proof Trees, Counter Example Trees; 3.4.5 Soundness of the Gentzen System G2 ; 3.4.6 The Search Procedure | |
| 505 | 8 | |a 3.4.7 Completeness of the Gentzen System G2 .4.8 Conjunctive and Disjunctive Normal Form; 3.4.9 Negation Normal Form; Problems; 3.5 Proof Theory for Infinite Sequents: Extended Completeness of G2 ; 3.5.1 Infinite Sequents; 3.5.2 The Search Procedure for Infinite Sequents; 3.5.3 König's Lemma; 3.5.4 Signed Formulae; 3.5.5 Hintikka Sets; 3.5.6 Extended Completeness of the Gentzen System G2 3.5.7 Compactness, Model Existence, Consistency; 3.5.8 Maximal Consistent Sets; Problems; 3.6 More on Gentzen Systems: The Cut Rule; 3.6.1 Using Auxiliary Lemmas in Proofs; 3.6.2 The Gentzen System LK2 | |
| 505 | 8 | |a 3.6.3 Logical Equivalence of G2 LK2 and LK2 -- {cut}3.6.4 Gentzen's Hauptsatz for LK2 (Cut elimination theorem for LK'); 3.6.5 Characterization of Consistency in LK2 Problems; Notes and Suggestions for Further Reading; Chapter 4: Resolution in Propositional Logic; 4.1 Introduction; 4.2 A Special Gentzen System; 4.2.1 Definition of the System GCNF2 4.2.2 Soundness of the System GCNF2 4.2.3 Completeness of the System GCNF2 Problems; 4.3 The Resolution Method for Propositional Logic; 4.3.1 Resolution DAGs; 4.3.2 Definition of the Resolution Method for Propositional Logic | |
| 520 | 3 | |a 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 fir | |
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| 653 | 0 | |a MATHEMATICS / Logic | |
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| 653 | 0 | |a Automatic theorem proving | |
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| author | Gallier, Jean H. 1949- |
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| contents | Cover; Title page; Copyright; Table of Contents; Preface (Dover Edition); Preface (1985 Edition); How to use this Book as A Text; Chapter 1: Introduction; Chapter 2: Mathematical Preliminaries; 2.1 Relations, Functions, Partial Orders, Induction; 2.1.1 Relations; 2.1.2 Partial Functions, Total Functions; 2.1.3 Composition of Relations and Functions; 2.1.4 Injections, Surjections, Bijections; 2.1.5 Direct Image, Inverse Image; 2.1.6 Sequences; 2.1.7 Natural Numbers and Countability; 2.1.8 Equivalence Relations; 2.1.9 Partial and Total Orders; 2.1.10 Well-Founded Sets and Complete Induction 3.3.1 The Semantics of Propositions3.3.2 Satisfiability, Unsatisfiability, Tautologies; 3.3.3 Truth Functions and Functionally Complete Sets of Connectives; 3.3.4 Logical Equivalence and Boolean Algebras; * 3.3.5 NP-Complete Problems; Problems; 3.4 Proof Theory of Propositional Logic: The Gentzen System G2 3.4.1 Basic Idea: Searching for a Counter Example; 3.4.2 Sequents and the Gentzen System G'; 3.4.3 Falsifiable and Valid Sequents; 3.4.4 Axioms, Deduction Trees, Proof Trees, Counter Example Trees; 3.4.5 Soundness of the Gentzen System G2 ; 3.4.6 The Search Procedure 3.4.7 Completeness of the Gentzen System G2 .4.8 Conjunctive and Disjunctive Normal Form; 3.4.9 Negation Normal Form; Problems; 3.5 Proof Theory for Infinite Sequents: Extended Completeness of G2 ; 3.5.1 Infinite Sequents; 3.5.2 The Search Procedure for Infinite Sequents; 3.5.3 König's Lemma; 3.5.4 Signed Formulae; 3.5.5 Hintikka Sets; 3.5.6 Extended Completeness of the Gentzen System G2 3.5.7 Compactness, Model Existence, Consistency; 3.5.8 Maximal Consistent Sets; Problems; 3.6 More on Gentzen Systems: The Cut Rule; 3.6.1 Using Auxiliary Lemmas in Proofs; 3.6.2 The Gentzen System LK2 3.6.3 Logical Equivalence of G2 LK2 and LK2 -- {cut}3.6.4 Gentzen's Hauptsatz for LK2 (Cut elimination theorem for LK'); 3.6.5 Characterization of Consistency in LK2 Problems; Notes and Suggestions for Further Reading; Chapter 4: Resolution in Propositional Logic; 4.1 Introduction; 4.2 A Special Gentzen System; 4.2.1 Definition of the System GCNF2 4.2.2 Soundness of the System GCNF2 4.2.3 Completeness of the System GCNF2 Problems; 4.3 The Resolution Method for Propositional Logic; 4.3.1 Resolution DAGs; 4.3.2 Definition of the Resolution Method for Propositional Logic |
| ctrlnum | (OCoLC)1334046004 (DE-599)BVBBV048294601 |
| discipline | Informatik Mathematik |
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| edition | Second edition, Dover edition |
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| id | DE-604.BV048294601 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:04:42Z |
| indexdate | 2024-07-10T09:34:27Z |
| institution | BVB |
| isbn | 9780486805085 0486805085 |
| language | English |
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| record_format | marc |
| series2 | Dover books on computer science |
| spelling | Gallier, Jean H. 1949- Verfasser (DE-588)122585615 aut Logic for computer science foundations of automatic theorem proving Jean H. Gallier, Department of Computer and Information Science University of Pennsylvania Second edition, Dover edition Mineola, New York Dover Publications, Inc. 2015 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Dover books on computer science "This Dover edition, first published in 2015, is an unabridged republication of the revised 2003 online edition of the work originally published by Harper & Row, New York, in 1986. A new Preface to the Dover Edition has been specially prepared for this volume." Cover; Title page; Copyright; Table of Contents; Preface (Dover Edition); Preface (1985 Edition); How to use this Book as A Text; Chapter 1: Introduction; Chapter 2: Mathematical Preliminaries; 2.1 Relations, Functions, Partial Orders, Induction; 2.1.1 Relations; 2.1.2 Partial Functions, Total Functions; 2.1.3 Composition of Relations and Functions; 2.1.4 Injections, Surjections, Bijections; 2.1.5 Direct Image, Inverse Image; 2.1.6 Sequences; 2.1.7 Natural Numbers and Countability; 2.1.8 Equivalence Relations; 2.1.9 Partial and Total Orders; 2.1.10 Well-Founded Sets and Complete Induction 3.3.1 The Semantics of Propositions3.3.2 Satisfiability, Unsatisfiability, Tautologies; 3.3.3 Truth Functions and Functionally Complete Sets of Connectives; 3.3.4 Logical Equivalence and Boolean Algebras; * 3.3.5 NP-Complete Problems; Problems; 3.4 Proof Theory of Propositional Logic: The Gentzen System G2 3.4.1 Basic Idea: Searching for a Counter Example; 3.4.2 Sequents and the Gentzen System G'; 3.4.3 Falsifiable and Valid Sequents; 3.4.4 Axioms, Deduction Trees, Proof Trees, Counter Example Trees; 3.4.5 Soundness of the Gentzen System G2 ; 3.4.6 The Search Procedure 3.4.7 Completeness of the Gentzen System G2 .4.8 Conjunctive and Disjunctive Normal Form; 3.4.9 Negation Normal Form; Problems; 3.5 Proof Theory for Infinite Sequents: Extended Completeness of G2 ; 3.5.1 Infinite Sequents; 3.5.2 The Search Procedure for Infinite Sequents; 3.5.3 König's Lemma; 3.5.4 Signed Formulae; 3.5.5 Hintikka Sets; 3.5.6 Extended Completeness of the Gentzen System G2 3.5.7 Compactness, Model Existence, Consistency; 3.5.8 Maximal Consistent Sets; Problems; 3.6 More on Gentzen Systems: The Cut Rule; 3.6.1 Using Auxiliary Lemmas in Proofs; 3.6.2 The Gentzen System LK2 3.6.3 Logical Equivalence of G2 LK2 and LK2 -- {cut}3.6.4 Gentzen's Hauptsatz for LK2 (Cut elimination theorem for LK'); 3.6.5 Characterization of Consistency in LK2 Problems; Notes and Suggestions for Further Reading; Chapter 4: Resolution in Propositional Logic; 4.1 Introduction; 4.2 A Special Gentzen System; 4.2.1 Definition of the System GCNF2 4.2.2 Soundness of the System GCNF2 4.2.3 Completeness of the System GCNF2 Problems; 4.3 The Resolution Method for Propositional Logic; 4.3.1 Resolution DAGs; 4.3.2 Definition of the Resolution Method for Propositional Logic 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 fir Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Automatic theorem proving Logic, Symbolic and mathematical Théorèmes / Démonstration automatique Logique symbolique et mathématique MATHEMATICS / General MATHEMATICS / Logic COMPUTERS / Computer Science Electronic books Automatisches Beweisverfahren (DE-588)4069034-9 s Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als 978-0-486-78082-5 Gallier, Jean H. Logic for Computer Science : Foundations of Automatic Theorem Proving, Second Edition Newburyport : Dover Publications, ©2015 Druck-Ausgabe, Paperback 978-0-486-78082-5 0-486-78082-1 |
| spellingShingle | Gallier, Jean H. 1949- Logic for computer science foundations of automatic theorem proving Cover; Title page; Copyright; Table of Contents; Preface (Dover Edition); Preface (1985 Edition); How to use this Book as A Text; Chapter 1: Introduction; Chapter 2: Mathematical Preliminaries; 2.1 Relations, Functions, Partial Orders, Induction; 2.1.1 Relations; 2.1.2 Partial Functions, Total Functions; 2.1.3 Composition of Relations and Functions; 2.1.4 Injections, Surjections, Bijections; 2.1.5 Direct Image, Inverse Image; 2.1.6 Sequences; 2.1.7 Natural Numbers and Countability; 2.1.8 Equivalence Relations; 2.1.9 Partial and Total Orders; 2.1.10 Well-Founded Sets and Complete Induction 3.3.1 The Semantics of Propositions3.3.2 Satisfiability, Unsatisfiability, Tautologies; 3.3.3 Truth Functions and Functionally Complete Sets of Connectives; 3.3.4 Logical Equivalence and Boolean Algebras; * 3.3.5 NP-Complete Problems; Problems; 3.4 Proof Theory of Propositional Logic: The Gentzen System G2 3.4.1 Basic Idea: Searching for a Counter Example; 3.4.2 Sequents and the Gentzen System G'; 3.4.3 Falsifiable and Valid Sequents; 3.4.4 Axioms, Deduction Trees, Proof Trees, Counter Example Trees; 3.4.5 Soundness of the Gentzen System G2 ; 3.4.6 The Search Procedure 3.4.7 Completeness of the Gentzen System G2 .4.8 Conjunctive and Disjunctive Normal Form; 3.4.9 Negation Normal Form; Problems; 3.5 Proof Theory for Infinite Sequents: Extended Completeness of G2 ; 3.5.1 Infinite Sequents; 3.5.2 The Search Procedure for Infinite Sequents; 3.5.3 König's Lemma; 3.5.4 Signed Formulae; 3.5.5 Hintikka Sets; 3.5.6 Extended Completeness of the Gentzen System G2 3.5.7 Compactness, Model Existence, Consistency; 3.5.8 Maximal Consistent Sets; Problems; 3.6 More on Gentzen Systems: The Cut Rule; 3.6.1 Using Auxiliary Lemmas in Proofs; 3.6.2 The Gentzen System LK2 3.6.3 Logical Equivalence of G2 LK2 and LK2 -- {cut}3.6.4 Gentzen's Hauptsatz for LK2 (Cut elimination theorem for LK'); 3.6.5 Characterization of Consistency in LK2 Problems; Notes and Suggestions for Further Reading; Chapter 4: Resolution in Propositional Logic; 4.1 Introduction; 4.2 A Special Gentzen System; 4.2.1 Definition of the System GCNF2 4.2.2 Soundness of the System GCNF2 4.2.3 Completeness of the System GCNF2 Problems; 4.3 The Resolution Method for Propositional Logic; 4.3.1 Resolution DAGs; 4.3.2 Definition of the Resolution Method for Propositional Logic Automatisches Beweisverfahren (DE-588)4069034-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4069034-9 (DE-588)4037951-6 |
| title | Logic for computer science foundations of automatic theorem proving |
| title_auth | Logic for computer science foundations of automatic theorem proving |
| title_exact_search | Logic for computer science foundations of automatic theorem proving |
| title_exact_search_txtP | Logic for computer science foundations of automatic theorem proving |
| title_full | Logic for computer science foundations of automatic theorem proving Jean H. Gallier, Department of Computer and Information Science University of Pennsylvania |
| title_fullStr | Logic for computer science foundations of automatic theorem proving Jean H. Gallier, Department of Computer and Information Science University of Pennsylvania |
| title_full_unstemmed | Logic for computer science foundations of automatic theorem proving Jean H. Gallier, Department of Computer and Information Science University of Pennsylvania |
| title_short | Logic for computer science |
| title_sort | logic for computer science foundations of automatic theorem proving |
| title_sub | foundations of automatic theorem proving |
| topic | Automatisches Beweisverfahren (DE-588)4069034-9 gnd Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Automatisches Beweisverfahren Mathematische Logik |
| work_keys_str_mv | AT gallierjeanh logicforcomputersciencefoundationsofautomatictheoremproving |