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This book constitutes the proceedings of the 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 32 papers presented in this volume were carefully reviewed and selected from 101 submissions. They were organized in topical sections named: coherence spaces and higher-order computation; algebra and coalgebra; games and automata; automata, logic and formal languages; proof theory; probability; concurrency; lambda calculus and constructive proof; and semantics and category theory.
This book is a sympathetic reconstruction of Henri Poincar's anti-realist philosophy of mathematics. Although Poincar is recognized as the greatest mathematician of the late 19th century, his contribution to the philosophy of mathematics is not highly regarded. Many regard his remarks as idiosyncratic, and based upon a misunderstanding of logic and logicism. This book argues that Poincar's critiques are not based on misunderstanding; rather, they are grounded in a coherent and attractive foundation of neo-Kantian constructivism.
This two-volume work brings together a comprehensive selection of mathematical works from the period 1707-1930. During this time the foundations of modern mathematics were laid, and From Kant to Hilbert provides an overview of the foundational work in each of the main branches of mathmeatics with narratives showing how they were linked. Now available as a separate volume.
Boolean algebras underlie many central constructions of analysis, logic, probability theory, and cybernetics. This book concentrates on the analytical aspects of their theory and application, which distinguishes it among other sources. Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.
The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods and highlights the rich relationships between them and integral calculus. The present book aims to be exhaustive since it analyzes the works of all major inventors of methods of indivisibles during the seventeenth century, from Kepler to Leibniz. It takes into account the rich existing literature usually devoted to a single author. This book results from the joint work of a team of specialists able to browse through this entire important episode in the history of mathematics and to comment it. The list of authors involved in indivisibles ́ field is probably sufficient to realize the richness of this attempt; one meets Kepler, Cavalieri, Galileo, Torricelli, Gregoire de Saint Vincent, Descartes, Roberval, Pascal, Tacquet, Lalouvère, Guldin, Barrow, Mengoli, Wallis, Leibniz, Newton.
This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm sele
This innovative volume investigates the meaning of ‘something’ in different recent philosophical traditions in order to rethink the logic and the unity of ontology, without forgetting to compare these views to earlier significative accounts in the history of philosophy. In fact, the revival of interest in “something” in the 19th and 20th centuries as well as in contemporary philosophy can easily be accounted for: it affords the possibility for asking the question: what is there? without engaging in predefined speculative assumptions The issue about “something” seems to avoid any naive approach to the question about what there is, so that it is treated in two main contemporary philosophical trends: “material ontology”, which aims at taking “inventory” of what there is, of everything that is; and “formal ontology”, which analyses the structural features of all there is, whatever it is. The volume advances cutting-edge debates on what is the first et the most general item in ontology, that is to say “something”, because the relevant features of the conceptual core of something are: non-nothingness, otherness. Something means that one being is different from others. The relationality belongs to something.: Therefore, the volume advances cutting-edge debates in phenomenology, analytic philosophy, formal and material ontology, traditional metaphysics.