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Orders: Description and Roles
Orders: Description and Roles
The Theory of Models
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders ...
The Lvov-Warsaw School. Past and Present
This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
Sets and Extensions in the Twentieth Century
Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights
Learning and Geometry: Computational Approaches
The field of computational learning theory arose out of the desire to for mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However...
A Shorter Model Theory
This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
Foundations of Data Science
Covers mathematical and algorithmic foundations of data science: machine learning, high-dimensional geometry, and analysis of large networks.
Theory and Application of Graph Transformations
Theareaofgraphtransformationoriginatedinthelate1960sunderthename “graph grammars” – the main motivation came from practical considerations concerning pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph transformation has grown impressively. The areas include: software speci?cation and development, VLSI layout schemes, database design, modeling of concurrent systems, m- sively parallel computer architectures, logic programming, computer animation, developmentalbiology,musiccomposition,distributedsystems,speci?cationl- guages, software and web engineering, and visual languages. As a matter of fact, graph transfo...
Petri Net Synthesis
This book is a comprehensive, systematic survey of the synthesis problem, and of region theory which underlies its solution, covering the related theory, algorithms, and applications. The authors focus on safe Petri nets and place/transition nets (P/T-nets), treating synthesis as an automated process which, given behavioural specifications or partial specifications of a system to be realized, decides whether the specifications are feasible, and then produces a Petri net realizing them exactly, or if this is not possible produces a Petri net realizing an optimal approximation of the specifications. In Part I the authors introduce elementary net synthesis. In Part II they explain variations of...
Neural Network Design and the Complexity of Learning
Using the tools of complexity theory, Stephen Judd develops a formal description of associative learning in connectionist networks. He rigorously exposes the computational difficulties in training neural networks and explores how certain design principles will or will not make the problems easier.Judd looks beyond the scope of any one particular learning rule, at a level above the details of neurons. There he finds new issues that arise when great numbers of neurons are employed and he offers fresh insights into design principles that could guide the construction of artificial and biological neural networks.The first part of the book describes the motivations and goals of the study and relat...
