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In contrast to the prevailing tradition in epistemology, the focus in this book is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief.

Monotonic functions --- Inference (Logic)

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Monotonic functions. --- Differentiable dynamical systems.

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Complex analysis --- 517.51 --- Functions of a real variable. Real functions --- Analytic functions. --- Monotonic functions. --- Analytic continuation. --- 517.51 Functions of a real variable. Real functions

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Various generalizations of the classical concept of a convex function have been introduced, especially during the second half of the 20th century. Generalized convex functions are the many nonconvex functions which share at least one of the valuable properties of convex functions. Apart from their theoretical interest, they are often more suitable than convex functions to describe real-word problems in disciplines such as economics, engineering, management science, probability theory and in other applied sciences. More recently, generalized monotone maps which are closely related to generalized convex functions have also been studied extensively. While initial efforts to generalize convexity and monotonicity were limited to only a few research centers, today there are numerous researchers throughout the world and in various disciplines engaged in theoretical and applied studies of generalized convexity/monotonicity (see http://www.genconv.org). The Handbook offers a systematic and thorough exposition of the theory and applications of the various aspects of generalized convexity and generalized monotonicity. It is aimed at the non-expert, for whom it provides a detailed introduction, as well as at the expert who seeks to learn about the latest developments and references in his research area. Results in this fast growing field are contained in a large number of scientific papers which appeared in a variety of professional journals, partially due to the interdisciplinary nature of the subject matter. Each of its fourteen chapters is written by leading experts of the respective research area starting from the very basics and moving on to the state of the art of the subject. Each chapter is complemented by a comprehensive bibliography which will assist the non-expert and expert alike.

Convex functions. --- Monotonic functions. --- Functions, Monotonic --- Functions of real variables --- Functions, Convex --- Convex functions --- Monotonic functions --- Mathematics. --- Real Functions. --- Game Theory, Economics, Social and Behav. Sciences. --- Operations Research, Management Science. --- Math --- Science --- Functions of real variables. --- Game theory. --- Operations research. --- Management science. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Real variables --- Functions of complex variables --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory

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In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.

Monotone operators. --- Monotonic functions. --- Banach spaces. --- Opérateurs monotones --- Fonctions monotones --- Banach, Espaces de --- Monotone operators --- Monotonic functions --- Banach spaces --- Duality theory (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Maxima and minima. --- Opérateurs monotones --- EPUB-LIV-FT SPRINGER-B --- Functions, Monotonic --- Minima --- Mathematics. --- Functional analysis. --- Operator theory. --- Calculus of variations. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Functions of real variables --- Operator theory --- Algebra --- Mathematical analysis --- Topology --- Functions of complex variables --- Generalized spaces --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis