Complicated Methods Of Logical Analysis Based On Simple Mathematics

Those who want to understand logic, if they manage to pass at least an initial, though far from simple, modern course of study, eventually conclude that practically logic consists in formulating premises and a taken-from-nowhere assertion in an incomprehensible language and then proving or disproving cause-consequence links between them. Conversely, many topical tasks of logical analysis, such as forming and testing hypotheses, inferring consequences with predefined properties, and searching for, and analysis of, logical errors and inconsistencies in reasoning, among others, are outside the scope of this discourse. They are scattered haphazardly in works on theory of argumentation, non-classical logics, and artificial intelligence. This book demonstrates the capabilities of two relatively simple mathematical systems developed by the authors, namely E-structures and n-tuple algebra, which allow the modelling of various types of reasoning and solve the above and some other tasks of logical analysis.

Hybrid systems are models for complex physical systems and have become a widely used concept for understanding their behavior. Many applications are safety-critical, including car, railway, and air traffic control, robotics, physical–chemical process control, and biomedical devices. Hybrid systems analysis studies how we can build computerized controllers for physical systems which are guaranteed to meet their design goals. The author gives a unique, logic-based perspective on hybrid systems analysis. It is the first book that leverages the power of logic for hybrid systems. The author develops a coherent logical approach for systematic hybrid systems analysis, covering its theory, practice, and applications. It is further shown how the developed verification techniques can be used to study air traffic and railway control systems. This book is intended for researchers, postgraduates, and professionals who are interested in hybrid systems analysis, cyberphysical or embedded systems design, logic and theorem proving, or transportation and automation.

First published in 2000. This is Volume II of six in the Library of Philosophy series on the Philosophy of Science. Written in 1938, philosophical systems which employ logical methods almost exclusively would undoubtedly be expected to produce non-empirical results. If, however, logic is taken simply as a method of connecting meanings it is not difficult to reconcile logical methods with empirical results. If logical formular, in other words, assert nothing about the meanings of propositions, but simply show how such meanings are connected, then an empiricism based on a logical analysis of meanings is not inconsistent. This is what the Logical Positivists have attempted to do. This book looks at two areas: the foundations of a scientific method free from metaphysics, and the elimination of pseudo-concepts introduced by metaphysics into science and philosophy.

Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This monograph collects some fundamental mathematical techniques that are required for the analysis of algorithms. It builds on the fundamentals of combinatorial analysis and complex variable theory to present many of the major paradigms used in the precise analysis of algorithms, emphasizing the more difficult notions. The authors cover recurrence relations, operator methods, and asymptotic analysis in a format that is concise enough for easy reference yet detailed enough for those with little background with the material.

Today the Internet is entering a new stage which will have a much stronger impact on the daily lives of all kinds of organizations. The next communication paradigm offers an improved access to mobility information, offering people and all organizations that deal with mobile devices the ability to access information whenever and wherever necessary. We really are at the edge of a new technological revolution, based on the ubiquity of information through the use of mobile devices and telecommunications. Furthermore, historical tendencies lead us to believe that the impact both on people and on organizations of this technological wave will be both faster and more powerful than any previous one. To the individual, information ubiquity results in the necessity to have immediate access to information. The strategic tactic and operational impact in organizations will therefore be incomparably deeper than in previous organizational management change using technology such as total quality management or business process re-engineering. This book acknowledges that it is crucial to find new organisational security approaches in the context of increasing dependency on the new technological wave which is building an information, communication and knowledge society.

Philosophy, from the earliest times, has made greater claims, and achieved fewer results, than any other branch of learning. Ever since Thales said that all is water, philosophers have been ready with glib assertions about the sum-total of things; and equally glib denials have come from other philosophers ever since Thales was contradicted by Anaximander. I believe that the time has now arrived when this unsatisfactory state of things can be brought to an end.

DigiCat Publishing presents to you this special edition of "Our Knowledge of the External World as a Field for Scientific Method in Philosophy" by Bertrand Russell. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.