Handbook of Automated Reasoning, Volume 1Alan 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
Leo Bachmair and Harald Ganzinger 1 2 Introduction Preliminaries | 22 |
Standard Resolution | 28 |
A Framework for SaturationBased Theorem Proving | 34 |
5 | 39 |
General Resolution | 46 |
6 | 48 |
Basic Resolution Strategies | 59 |
Refined Techniques for Defining Orderings and Selection Functions | 66 |
TERM INDEXING | 438 |
UNIFICATION THEORY | 445 |
Equational unification | 469 |
Syntactic methods for Eunification | 488 |
Semantic approaches to Eunification | 503 |
SOLVING NUMERICAL CONSTRAINTS | 504 |
Further topics | 519 |
Description Logics | 521 |
Global Theorem Proving Methods | 84 |
HANDBOOK OF AUTOMATED REASONING | 94 |
RESOLUTION DECISION PROCEDURES | 95 |
19 | 96 |
98 | |
Reiner Hähnle | 101 |
Resolution decision procedures for description logics | 102 |
28 | 103 |
34 | 150 |
CONNECTIONS IN NONCLASSICAL LOGICS | 175 |
THE INVERSE METHOD | 179 |
Conclusion | 198 |
46 | 265 |
103 | 266 |
MODEL ELIMINATION AND CONNECTION | 267 |
1 | 273 |
Introduction | 277 |
Classification of proof systems for manyvalued logics | 307 |
Concept index | 325 |
Optimization of transformation rules | 328 |
59 | 329 |
COMPUTING SMALL CLAUSE NORMAL FORMS | 335 |
2015 | 351 |
Skolemization | 352 |
PARAMODULATIONBASED THEOREM PROVING | 371 |
Conclusion | 380 |
Paramodulation calculi | 385 |
Saturation procedures | 399 |
Paramodulation with constrained clauses | 414 |
Extensions | 427 |
1009 | 524 |
66 | 526 |
Termination Properties | 535 |
EQUALITY REASONING IN SEQUENTBASED CALCULI | 611 |
84 | 645 |
AUTOMATED REASONING IN GEOMETRY | 693 |
89 | 695 |
699 | |
HANDBOOK OF AUTOMATED REASONING | 707 |
Linear diophantine constraints | 751 |
Gilles Dowek | 822 |
827 | |
828 | |
829 | |
THE AUTOMATION OF PROOF BY MATHEMATICAL | 845 |
LOGICAL FRAMEWORKS | 847 |
Description Logics and Propositional Dynamic Logics | 889 |
904 | |
INDUCTIONLESS INDUCTION | 913 |
Background | 918 |
98 | 950 |
Ground Reducibility | 957 |
958 | |
961 | |
963 | |
964 | |
965 | |
966 | |
968 | |
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Handbook of Automated Reasoning, Volume 2 John Alan Robinson,Andreĭ Voronkov No preview available - 2001 |
Common terms and phrases
algebraic algorithm applied atom Automated Deduction Automated Reasoning axioms Bachmair branch calculus chapter closure complete Computer Science consider constraint contains critical pair defined DEFINITION denote derivation Dershowitz equality equational theory equivalent example extension step finite first-order first-order logic free variables function symbols Ganzinger geometry Gröbner basis ground instances Herbrand Horn clauses induction rule inference rules inference system intuitionistic logic inverse method Kapur Lecture Notes lemma linear literals logic programming minimal modal logics multiset negation normal form Nieuwenhuis nodes normal form Notes in Computer obtained occur paramodulation path ordering polynomial positive premise quantifier quantifier elimination recursive redundant refutation renaming restrictions rewrite rules rewrite system satisfiable saturated Section selection function semantic sequent calculus set of clauses signed formulas simplification simultaneous rigid E-unification Skolem solution Springer-Verlag subformula substitution subterm superposition tableau proof techniques termination theorem proving transformation unifier unsatisfiable
Popular passages
Page 824 - M.-F. ROY A New Algorithm to Find a Point in Every Cell Defined by a Family of Polynomials in "Quantifier Elimination and Cylindrical Algebraic Decomposition", B.