Handbook of Automated Reasoning, Volume 2Alan J.A. Robinson, Andrei Voronkov Automated reasoning has matured into one of the most advanced areas of computer science. It is used in many areas of the field, including software and hardware verification, logic and functional programming, formal methods, knowledge representation, deductive databases, and artificial intelligence. This handbook presents an overview of the fundamental ideas, techniques, and methods in automated reasoning and its applications. The material covers both theory and implementation. In addition to traditional topics, the book covers material that bridges the gap between automated reasoning and related areas. Examples include model checking, nonmonotonic reasoning, numerical constraints, description logics, and implementation of declarative programming languages. The book consists of eight parts. After an overview of the early history of automated deduction, the areas covered are reasoning methods in first-order logic; equality and other built-in theories; methods of automated reasoning using induction; higher-order logic, which is used in a number of automatic and interactive proof-development systems; automated reasoning in nonclassical logics; decidable classes and model building; and implementation-related questions. |
Contents
REWRITING 535 | 999 |
HANDBOOK OF AUTOMATED REASONING | 1000 |
| 1005 | |
| 1009 | |
HigherOrder Unification and Matching | 1011 |
Terminology 541 | 1013 |
Induction | 1020 |
Undecidability | 1024 |
Firstorder intuitionistic logic | 1545 |
The S5 family | 1567 |
93 | 1571 |
Part II Classical Logic | 1574 |
Introduction 275 | 1581 |
Unrestricted Model Reasoning | 1598 |
Beyond Basic Description Logics | 1619 |
MODEL CHECKING | 1635 |
Decidable Subcases | 1041 |
Unification in Acalculus with Dependent Types | 1049 |
Bibliography | 1054 |
Termination Properties 546 | 1055 |
COMPUTING SMALL CLAUSE NORMAL FORMS | 1058 |
| 1061 | |
3 | 1063 |
Introduction | 1087 |
Inductive Proof Techniques | 1108 |
Preliminaries 104 | 1140 |
9 | 1141 |
12 | 1142 |
15 | 1144 |
PROOFASSISTANTS USING DEPENDENT TYPE SYSTEMS | 1149 |
Interactive Theorem Proving | 1155 |
21 | 1163 |
Inductive Theorem Provers | 1180 |
Conclusion | 1192 |
28 | 1200 |
34 | 1201 |
General Nonmonotonic Logics 2 Automating General Nonmonotonic Logics 3 From Automated Reasoning to Disjunctive Logic Programming 4 No... | 1241 |
Implementing Nonmonotonic Semantics 6 Benchmarks | 1242 |
46 | 1286 |
Bibliography Index | 1340 |
reasoning classically about finitelyvalued logics | 1355 |
Signed resolution | 1379 |
An example | 1389 |
Optimization of transformation rules | 1393 |
Remarks on infinitelyvalued logics | 1395 |
Bibliography | 1396 |
59 | 1399 |
| 1401 | |
IN CLASSICAL LOGIC 1403 Hans Jürgen Ohlbach Andreas Nonnengart Maarten de Rijke and Dov M Gabbay 1 Introduction 1405 2 Background 3 ... | 1403 |
The standard relational translation | 1431 |
84 | 1437 |
The functional translation | 1445 |
THE INVERSE METHOD 179 | 1478 |
91 | 1479 |
1410 | 1484 |
1423 | 1485 |
1440 | 1486 |
CONNECTIONS IN NONCLASSICAL LOGICS | 1487 |
Applying the recipe to nonclassical logics 209 | 1495 |
Labelled systems | 1516 |
Compositionality and Modular Verification | 1636 |
Second Order Languages | 1654 |
Model Transformations and Properties | 1670 |
Completeness | 1689 |
Basic Model Checking Algorithms | 1711 |
Notation and Definitions 278 | 1791 |
5 | 1802 |
Normal Forms in Nonclassical Logics 323 | 1840 |
TERM INDEXING | 1853 |
Path indexing | 1859 |
6 | 1876 |
Adaptive automata | 1896 |
Automatadriven indexing | 1900 |
Automatadriven indexing | 1908 |
Substitution trees | 1917 |
Substitution trees | 1919 |
Unification factoring | 1924 |
Multiterm indexing | 1927 |
Issues in perfect filtering | 1934 |
Elements of term indexing | 1943 |
Indexing in practice | 1951 |
Conclusion | 1955 |
RESOLUTION THEOREM PROVING Leo Bachmair and Harald Ganzinger 1 2 | 1957 |
COMBINING SUPERPOSITION Sorts and SplITTING | 1965 |
Introduction | 1968 |
Standard Resolution | 1990 |
A Framework for SaturationBased Theorem Proving 5 General Resolution | 1995 |
Simplification | 1997 |
Bibliographic Notes | 2008 |
Basic Resolution Strategies | 2009 |
Refined Techniques for Defining Orderings and Selection Functions 8 Global Theorem Proving Methods 9 FirstOrder Resolution Methods | 2010 |
Preliminaries | 2015 |
Effective Saturation of FirstOrder Theories 11 Concluding Remarks Bibliography Index | 2016 |
5 | 2025 |
Further Structural Refinements of Clausal Tableaux | 2036 |
Shortening of Proofs | 2049 |
Completeness of Connection Tableaux | 2062 |
Architectures of Model Elimination Implementations | 2070 |
Implementation of Refinements by Constraints | 2092 |
Experimental Results | 2102 |
Outlook | 2107 |
AUTOMATED REASONING IN GEOMETRY 707 | 2115 |
| 2117 | |
Other editions - View all
Handbook of Automated Reasoning Robinson, John Alan Robinson,Andreĭ Voronkov No preview available - 2001 |
Common terms and phrases
algorithm applied Artificial Intelligence atomic automata Automated Reasoning automated theorem proving axiom binary bisimulation calculus classical clause set complete Computer Science concept construction contains corresponding decision procedure default default logic defined definition denote derivation description logics disjunctive domain encoding equations equivalent example expressions extension first-order logic formula free variable higher-order higher-order logic higher-order unification implementation indexed terms induction inference intuitionistic intuitionistic logic knowledge base labelled language Lemma literals logic programming logical framework M₁ method modal logic model checking natural deduction negation node nonmonotonic normal form occur operator predicate predicate logic prefix problem Proc proof propositional quantifiers query term relation representation resolution retrieval role rules satisfiable semantics sequent sequent calculus skeleton Skolem Springer stable model sub-formulas substitution subsumption t₁ tableau techniques temporal logic theorem proving transition translation tree type theory unification unifier w₁