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AI(Artificial intelligence) --- Artificial intelligence --- Artificial thinking --- Artificiële intelligentie --- Automatic theorem proving --- Electronic brains --- Intellectronics --- Intelligence [Artificial ] --- Intelligence artificielle --- Intelligent machines --- Kunstmatige intelligentie --- Machine intelligence --- Theorema's--Automatische bewijsvoering --- Thinking [Artificial ] --- Théorèmes--Démonstration automatique --- Cerveaux électroniques --- Machines intelligentes --- Pensée artificielle --- Automatic theorem proving. --- Artificial intelligence. --- Unification --- Resolution --- Graph --- Prolog (langage de programmation) --- Induction --- Gentzen Calculus --- Logic

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Instantiation Theory presents a new, general unification algorithm that is of immediate use in building theorem provers and logic programming systems. Instantiation theory is the study of instantiation in an abstract context that is applicable to most commonly studied logical formalisms. The volume begins with a survey of general approaches to the study of instantiation, as found in tree systems, order-sorted algebras, algebraic theories, composita, and instantiation systems. A classification of instantiation systems is given, based on properties of substitutions, degree of type strictness, and well-foundedness of terms. Equational theories and the use of typed variables are studied in terms of quotient homomorphisms and embeddings, respectively. Every instantiation system is a quotient system of a subsystem of first-order term instantiation. The general unification algorithm is developed as an application of the basic theory. Its soundness is rigorously proved, and its completeness and efficiency are verfied for certain classes of instantiation systems. Appropriate applications of the algorithm include unification of first-order terms, order-sorted terms, and first-order formulas modulo alpha-conversion, as well as equational unification using simple congruences.

Automatic theorem proving --- Theorema's--Automatische bewijsvoering --- Théorèmes--Démonstration automatique --- 681.3*I23 --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Automatic theorem proving. --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Artificial intelligence. --- Information theory. --- Software engineering. --- Computer science. --- Algebra --- Computer software. --- Artificial Intelligence. --- Theory of Computation. --- Software Engineering/Programming and Operating Systems. --- Mathematical Logic and Formal Languages. --- Symbolic and Algebraic Manipulation. --- Algorithm Analysis and Problem Complexity. --- Data processing. --- Software, Computer --- Computer systems --- Informatics --- Science --- Computer software engineering --- Engineering --- Communication theory --- Communication --- Cybernetics --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers

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This book presents a strictly refereed collection of revised full papers selected from the papers accepted for the TYPES '94 Workshop, held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Bastad, Sweden, in June 1994. The 10 papers included address various aspects of developing computer-assisted proofs and programs using a logical framework. Type theory and three logical frameworks based on it are dealt with: ALF, Coq, and LEGO; other topics covered are metatheory, the Isabelle system, 2-calculus, proof checkers, and ZF set theory.

Automatic theorem proving --- Theorema's--Automatische bewijsvoering --- Théorèmes--Démonstration automatique --- Théorèmes --- Congresses. --- Démonstration automatique --- Congrès --- Théorèmes --- Démonstration automatique --- Congrès --- Software engineering. --- Computer science. --- Logic design. --- Artificial intelligence. --- Logic, Symbolic and mathematical. --- Software Engineering/Programming and Operating Systems. --- Mathematical Logic and Formal Languages. --- Logics and Meanings of Programs. --- Programming Languages, Compilers, Interpreters. --- Artificial Intelligence. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Informatics --- Science --- Computer software engineering --- Engineering

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The ability to draw inferences is a central operation in any artificial intelligence system. Automated reasoning is therefore among the traditional disciplines in AI. Theory reasoning is about techniques for combining automated reasoning systems with specialized and efficient modules for handling domain knowledge called background reasoners. Connection methods have proved to be a good choice for implementing high-speed automated reasoning systems. They are the starting point in this monograph,in which several theory reasoning versions are defined and related to each other. A major contribution of the book is a new technique of linear completion allowing for the automatic construction of background reasoners from a wide range of axiomatically given theories. The emphasis is on theoretical investigations, but implementation techniques based on Prolog are also covered.

Automatic theorem proving --- Computer Science --- Engineering & Applied Sciences --- Automatic theorem proving. --- Theorema's--Automatische bewijsvoering --- Théorèmes--Démonstration automatique --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Engineering. --- Computers. --- Mathematical logic. --- Artificial intelligence. --- Robotics. --- Automation. --- Robotics and Automation. --- Theory of Computation. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Mathematical Logic and Foundations. --- Artificial intelligence --- Proof theory --- Information theory. --- Computer science. --- Logic, Symbolic and mathematical. --- Artificial Intelligence. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Informatics --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Communication theory --- Communication --- Cybernetics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace --- Automatic factories --- Automatic production --- Computer control --- Engineering cybernetics --- Factories --- Industrial engineering --- Mechanization --- Assembly-line methods --- Automatic control --- Automatic machinery --- CAD/CAM systems --- Robotics --- Automation