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681.3*I23 --- 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) --- Fuzzy

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Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009.

Philosophy of science --- Probabilities --- Induction (Mathematics) --- Mathematical statistics --- History. --- Arts and Humanities --- Philosophy --- Induction (Logic) --- Mathematics --- Mathematical induction --- Probabilités --- Induction (mathématiques) --- Statistique mathématique --- Histoire --- History

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Automatic theorem proving --- -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) --- Automated theorem proving --- Theorem proving, Automated --- Theorem proving, Automatic --- Artificial intelligence --- Proof theory --- Congresses --- 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) --- Informatique

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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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Programming --- Mathematical logic --- Logic Programming --- Logic programming --- 681.3*I23 --- Computer programming --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Logic programming. --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence)