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Lukasiewicz's Logics and Prime Numbers
Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Lukasiewicz logics Ln+1. Prime numbers are defined in algebraic-logical terms (Finn's theorem) and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they have tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Ln+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Lukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers.
Advanced Łukasiewicz calculus and MV-algebras
This is a continuation of Vol. 7 of Trends in Logic. It wil cover the wealth of recent developments of Lukasiewicz Logic and their algebras (Chang MV-algebras), with particular reference to (de Finetti) coherent evaluation of continuously valued events, (Renyi) conditionals for such events, related algorithms.
The Concept of Causality in the Lvov-Warsaw School
The kernel of this volume is an English translation of Jan Łukasiewicz’s classic work on the concept of cause (1906). It is the starting point for analytical considerations on causality of two generations of philosophers belonging to the tradition of the Lvov-Warsaw School.
Lukasiewicz-Moisil Algebras
The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.
Polish Scientific Philosophy: The Lvov-Warsaw School
One can often encounter an opinion that Polish scientific (or analytic) philosophy (or the Lvov-Warsaw School) deserves to be much better known than actually is. This book is thought as a response to such a claim. The papers collected in this volume are divided into two parts: Background and Influence and History and Systematics. However, there is no sharp borderline between themes which are touched in both parts. Generally speaking, all papers of the first part relate the Lvov-Warsaw School to some philosophical movements (Brentanism, phenomenology and Marxism) external to it whereas the papers collected in the second one focus on internal issues connected with the school (only Roberto Poli...
Kazimierz Twardowski: A Grammar for Philosophy
Kazimierz Twardowski (1866-1938) is the founder of the Lvov-Warsaw School with its strong tradition in logic and its scientific approach to philosophy. Twardowski’s unique way of doing philosophy, his method, is of central importance for understanding his impact as a teacher. This method can be understood as a philosophical grammar, which is also how Leibniz conceived his universal language of thought. Analytic philosophy in the twentieth century can be characterized by its opposition to psychologism, on the one hand, and its opposition to metaphysics, on the other. This is changing now, as questions within the philosophy of mind and metaphysics are raised by analytic philosophers today. Maria van der Schaar shows in her book that we can improve our analytic methods by making use of Twardowski’s philosophical grammar. Twardowski’s positive attitude to psychology and metaphysics may also help us to develop an analytic metaphysics and to get a better understanding of the relation between psychology and philosophy.
Fundamental Problems in Quantum Physics
For many physicists quantum theory contains strong conceptual difficulties, while for others the apparent conclusions about the reality of our physical world and the ways in which we discover that reality remain philosophically unacceptable. This book focuses on recent theoretical and experimental developments in the foundations of quantum physics, including topics such as the puzzles and paradoxes which appear when general relativity and quantum mechanics are combined; the emergence of classical properties from quantum mechanics; stochastic electrodynamics; EPR experiments and Bell's Theorem; the consistent histories approach and the problem of datum uniqueness in quantum mechanics; non-local measurements and teleportation of quantum states; quantum non-demolition measurements in optics and matter wave properties observed by neutron, electron and atomic interferometry. Audience: This volume is intended for graduate students of physics and those interested in the foundations of quantum theory.
Logic: Reference Book for Computer Scientists
The book gives all interested in computer science, a deep review of relevant aspects of logic. In its scope are classical and non-classical logics. The content will be valid as well for those interested in linguistic, philosophy and many other areas of research both in humane and technical branches of science as logic permeates all genuine realms of science. The book contains a substantial part of classical results in logic like those by Gödel, Tarski, Church and Rosser as well as later developments like many-valued logics, logics for knowledge engineering, first-order logics plus inductive definitions. The exposition is rigorous yet without unnecessary abstractionism, so it should be accessible to readers from many disciplines of science. Each chapter contains a problem section, and problems are borrowed from research publications which allows for passing additional information, and it allows readers to test their skills. Extensive bibliography of 270 positions directs readers to research works of importance.
Ceramic Materials for Electronics, Third Edition
The Third Edition of Ceramic Materials for Electronics studies a wide range of ceramic materials, including insulators, conductors, piezoelectrics, and ferroelectrics, through detailed discussion of their properties, characterization, fabrication, and applications in electronics. The author summarizes the latest trends and advancements in the field, and explores important topics such as ceramic thin film, functional device technology, and thick film technology. Edited by a leading expert on the subject, this new edition includes more than 150 pages of new information; restructured reference materials, figures, and tables; as well as additional device application-oriented segments.
