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"Induction is a pervasive tool in computer science and mathematics for defining objects and reasoning on them. Coinduction is the dual of induction and as such it brings in quite different tools. Today, it is widely used in computer science, but also in other fields, including artificial intelligence, cognitive science, mathematics, modal logics, philosophy and physics. The best known instance of coinduction is bisimulation, mainly employed to define and prove equalities among potentially infinite objects: processes, streams, non-well-founded sets, etc. This book presents bisimulation and coinduction: the fundamental concepts and techniques and the duality with induction. Each chapter contains exercises and selected solutions, enabling students to connect theory with practice. A special emphasis is placed on bisimulation as a behavioural equivalence for processes. Thus the book serves as an introduction to models for expressing processes (such as process calculi) and to the associated techniques of operational and algebraic analysis"--

Bisimulation. --- Coinduction (Mathematics) --- Modality (Logic) --- Induction (Mathematics) --- Computer science. --- Informatics --- Science --- Mathematical induction --- Induction (Logic) --- Mathematics --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- Mathematical coinduction

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This second volume is arranged in four sections: Analysis contains papers which compare the attributes of various approaches to uncertainty. Tools provides sufficient information for the reader to implement uncertainty calculations. Papers in the Theory section explain various approaches to uncertainty. The Applications section describes the difficulties involved in, and the results produced by, incorporating uncertainty into actual systems.

681.3*E4 --- 681.3*I23 --- Coding and information theory: data compaction and compression; formal modelsof communication; nonsecret encoding schemes--See also {681.3*H11} --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*E4 Coding and information theory: data compaction and compression; formal modelsof communication; nonsecret encoding schemes--See also {681.3*H11} --- Artificial intelligence. --- Problem solving. --- Uncertainty (Information theory) --- Measure of uncertainty (Information theory) --- Shannon's measure of uncertainty --- System uncertainty --- Information measurement --- Probabilities --- Questions and answers --- Methodology --- Psychology --- Decision making --- Executive functions (Neuropsychology) --- 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 --- Artificial intelligence --- Knowledge Representation --- Uncertainty

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The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of the application of logic to artificial intelligence and logic programming. The authors are chosen on an international basis and are leaders in the fields covered. Volume 5 is the last in this well-regarded series. Logic is now widely recognized as one of the foundational disciplines of computing. It has found applications in virtually all aspects of the subject, from software and hardware engineering to programming languages and artificial intelligence.

Logic programming. --- Computer programming --- 681.3*I2 --- 681.3*I23 --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I2 Artificial intelligence. AI --- Artificial intelligence. AI --- Logic programming --- Artificial intelligence --- Logic, Symbolic and mathematical --- 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 --- Knowledge, Theory of. --- Théorie de la connaissance. --- Informatique --- Computer science --- Logique mathématique --- Logique non monotone --- Nonmonotonic reasoning --- Artificial intelligence. --- Logic, Symbolic and mathematical. --- Théorie de la connaissance --- Computer science. --- Logique mathématique. --- Logique générale --- Epistemologie --- Logique modale --- Knowledge representation

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Logic's basic elements are unfolded in this book. The relation of and the transition from Logic to Logic Programming are analysed. With the use and the development of computers in the beginning of the 1950's, it soon became clear that computers could be used, not only for arithmetical computation, but also for symbolic computation. Hence, the first arithmetical computation programs, and the first programs created to answer elementary questions and prove simple theorems, were written simultaneously. The basic steps towards a general method based on Logic, were accomplished in 1965 by Robinson

Logic programming --- Logic, Symbolic and mathematical --- Programmation logique --- Logique symbolique et mathématique --- 681.3*D16 --- 681.3*F41 --- 681.3*I23 --- 681.3*I24 --- Computerwetenschap--?*D16 --- 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} --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- 681.3*I24 Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (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} --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer programming --- Logique symbolique et mathématique --- Logic programming. --- Logic, Symbolic and mathematical.

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The idea of knowledge bases lies at the heart of symbolic, or "traditional," artificial intelligence. A knowledge-based system decides how to act by running formal reasoning procedures over a body of explicitly represented knowledge--a knowledge base. The system is not programmed for specific tasks; rather, it is told what it needs to know and expected to infer the rest.This book is about the logic of such knowledge bases. It describes in detail the relationship between symbolic representations of knowledge and abstract states of knowledge, exploring along the way the foundations of knowledge, knowledge bases, knowledge-based systems, and knowledge representation and reasoning. Assuming some familiarity with first-order predicate logic, the book offers a new mathematical model of knowledge that is general and expressive yet more workable in practice than previous models. The book presents a style of semantic argument and formal analysis that would be cumbersome or completely impractical with other approaches. It also shows how to treat a knowledge base as an abstract data type, completely specified in an abstract way by the knowledge-level operations defined over it.

Théorie de la connaissance --- Logique mathématique --- Information, Théorie de l' --- Knowledge representation (Information theory) --- Expert systems (Computer science) --- Logic, Symbolic and mathematical. --- Logic, Symbolic and mathematical --- 681.3*I23 --- 681.3*I24 --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Representation of knowledge (Information theory) --- Artificial intelligence --- Information theory --- Knowledge-based systems (Computer science) --- Systems, Expert (Computer science) --- Computer systems --- Soft computing --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- Computer Science --- Engineering & Applied Sciences --- 681.3*I24 Knowledge representation formalisms and methods: frames and scripts; predicate logic; relation systems; representation languages; procedural and rule-based representations; semantic networks (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Expert systems (Computer science). --- Knowledge representation (Information theory). --- Théorie de la connaissance. --- Logique mathématique. --- Information, Théorie de l'. --- COMPUTER SCIENCE/Artificial Intelligence --- Théorie de la connaissance. --- Logique mathématique. --- Information, Théorie de l'.