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This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.

Mathematical logic --- logica --- wiskunde --- Model theory

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Artificial intelligence --- Logic, Symbolic and mathematical --- Intelligence artificielle --- Logique symbolique et mathématique --- Congresses. --- Congrès --- Computer Science --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mechanical Engineering --- 681.3*I2 --- 681.3*F41 --- 681.3*D16 --- Artificial intelligence. AI --- 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 techniques: Logic programming --- Information Technology --- Artificial Intelligence --- 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*I2 Artificial intelligence. AI --- Computer science. --- Computer programming. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Programming Techniques. --- Mathematical Logic and Formal Languages. --- 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 --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Informatics --- Science --- Programming --- Artificial Intelligence. --- JELIA

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Machine learning --- Apprentissage automatique --- Congresses. --- Congrès --- Computer Science --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- 681.3*I26 <063> --- 681.3*I2 --- 681.3*F22 --- 681.3*F41 --- 681.3*H28 --- Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32}--Congressen --- Artificial intelligence. AI --- Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- 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} --- Database applications --- Conferences - Meetings --- 681.3*I2 <063> --- 681.3*H2 <063> --- 681.3*J2 <063> --- 681.3*H3 <063> --- 681.3*G3 <063> --- 681.3*I7 <063> --- 681.3*F42 <063> --- Artificial intelligence. AI--Congressen --- Database management: security; integrity; protection--See also {?681.5*E5}--Congressen --- Physical sciences and engineering (Computer applications)--Congressen --- Information storage and retrieval--Congressen --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing)--Congressen --- Text processing (Computing methodologies)--See also {681.3*H4}--Congressen --- Grammars and other rewriting systems: decision problems; grammar types; parallel rewriting systems; parsing; thue systems (Mathematical logic and formal languages)--See also {681.3*D31}--Congressen --- Information Technology --- Artificial Intelligence --- 681.3*H28 Database applications --- 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*F22 Nonnumerical algorithms and problems: complexity of proof procedures; computations on discrete structures; geometrical problems and computations; pattern matching --See also {?681.3*E2-5}; {681.3*G2}; {?681.3*H2-3} --- 681.3*I2 Artificial intelligence. AI --- 681.3*I26 <063> Learning: analogies; concept learning; induction; knowledge acquisition; language acquisition; parameter learning (Artificial intelligence)--See also {681.3*K32}--Congressen --- 681.3*J2 <063> Physical sciences and engineering (Computer applications)--Congressen --- 681.3*I2 <063> Artificial intelligence. AI--Congressen --- Computer science. --- Algorithms. --- Mathematical logic. --- Database management. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Algorithm Analysis and Problem Complexity. --- Mathematical Logic and Formal Languages. --- Database Management. --- 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 --- Informatics --- Science --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algorism --- Algebra --- Arithmetic --- Foundations --- Computer software. --- Artificial Intelligence. --- Software, Computer --- Computer systems