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Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as

Mathematical logic --- Model theory. --- Logic, Symbolic and mathematical. --- Model theory --- Théorie des modèles --- ELSEVIER-B EPUB-LIV-FT --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, Symbolic and mathematical

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Axiomatic set theory --- Computer network protocols --- Computer science --- Théorie axiomatique des ensembles --- Protocoles de réseaux d'ordinateurs --- Informatique --- Mathematics --- Mathématiques --- #KVIV:BB --- 681.3*D33 --- 681.3*F41 --- Languages constructs: abstract data types; concurrent programming structures;control structures; coroutines (Programming languages) --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*D33 Languages constructs: abstract data types; concurrent programming structures;control structures; coroutines (Programming languages) --- Théorie axiomatique des ensembles --- Protocoles de réseaux d'ordinateurs --- Mathématiques --- Mathematics.

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512 --- Set theory --- Computer programming --- 681.3*F3 --- 681.3*F41 --- Computers --- Electronic computer programming --- Electronic data processing --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Algebra --- Logics and meanings of programs (Theory of computation) --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Programming --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F3 Logics and meanings of programs (Theory of computation) --- 512 Algebra --- Type Theory --- Parameterized --- Abstract data types (Computer science)

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The aim of this book is to reflect the substantial re- search done in Artificial Intelligence on sorts and types. The main contributions come from knowledge representation and theorem proving and important impulses come from the "application areas", i.e. natural language (understanding) systems, computational linguistics, and logic programming. The workshop brought together researchers from logic, theoretical computer science, theorem proving, knowledge representation, linguistics, logic programming and qualitative reasoning.

681.3*F41 --- 681.3*I20 --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Artificial intelligence (AI) in general; cognitive simulation; philosophical foundations --- 681.3*I20 Artificial intelligence (AI) in general; cognitive simulation; philosophical foundations --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Artificial intelligence --- Congresses --- Logic [Symbolic and mathematical ] --- Sorting (Electronic computers) --- Abstract data types (Computer science) --- Artificial intelligence - Congresses. --- Logic, Symbolic and mathematical - Congresses. --- Sorting (Electronic computers) - Congresses. --- Abstract data types (Computer science) - Congresses. --- Artificial intelligence. --- Computer science. --- Logic, Symbolic and mathematical. --- Artificial Intelligence. --- Mathematical Logic and Formal Languages. --- Mathematical Logic and Foundations. --- 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 --- Order Sorted --- Type --- Protos --- Lilog --- Kl One --- Lncs --- Lnai

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Termination proofs constitute a crucial part of program verification. Much research about termination has been done in the context of term rewriting systems. But until now there was little hope that termination proofs for nontrivial programs could be achieved automatically. This book gives a comprehensive discussion of the termination problem in the context of logic programming. Although logic programs pose special difficulties for termination proofs it turns out that automation of this task is obtainable to a much larger degree than for programs in imperative languages. A technique for the automatic derivation of termination proofs is presented in detail. The discussion of several nontrivial examples illustrates its range of applicability. The approach is based on the concept of declarative semantics, and thus makes use of an important feature of logic programming.

AI(Artificial intelligence) --- Artificial intelligence --- Artificial thinking --- Artificiële intelligentie --- Electronic brains --- Intellectronics --- Intelligence [Artificial ] --- Intelligence artificielle --- Intelligent machines --- Kunstmatige intelligentie --- Logic programming --- Logisch programmeren --- Logische programmering --- Machine intelligence --- Programmation logique --- Programmeren [Logisch ] --- Programming [Logic ] --- Thinking [Artificial ] --- 681.3*D24 --- 681.3*F31 --- 681.3*F41 --- 681.3*I2 --- Computer programming --- AI (Artificial intelligence) --- Intelligence, Artificial --- 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 --- Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31} --- Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Artificial intelligence. AI --- 681.3*I2 Artificial intelligence. AI --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F31 Specifying anf verifying and reasoning about programs: assertions; invariants; mechanical verification; pre- and post-conditions (Logics and meanings of programs)--See also {681.3*D21}; {681.3*D24}; {681.3*D31}; {681.3*E1} --- 681.3*D24 Program verification: assertion checkers; correctness proofs; reliability; validation (Software engineering)--See also {681.3*F31} --- Cerveaux électroniques --- Machines intelligentes --- Pensée artificielle --- Artificial intelligence. --- Logic programming. --- Computer science. --- Software engineering. --- Logic design. --- Artificial Intelligence. --- Programming Languages, Compilers, Interpreters. --- Software Engineering. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer software engineering --- Engineering --- Informatics --- Science