Matematisk logik

»Philosophy of Mathematics« is understood, in this book, as an effort to clarify such questions that mathematics itself raises but cannot answer with its own methods. These include, for example, questions about the ontological status of mathematical objects (e.g., what is the nature of mathematical objects?) and the epistemological status of mathematical theorems (e.g., from what sources do we draw when we prove mathematical theorems?). The answers given by Plato, Aristotle, Euclid, Descartes, Locke, Leibniz, Kant, Cantor, Frege, Dedekind, Hilbert and others will be studied in detail. This will lead us to deep insights, not only into the history of mathematics, but also into the conception of mathematics as it is commonly held in the present time.The book is a translation from the German, however revised and considerably expanded. Various chapters have been completely rewritten.

This contributed volume overviews recently presented approaches for carrying out QSPR/QSAR analysis by using a simplifying molecular input-line entry system (SMILES) to represent the molecular structure. In contrast to traditional SMILES, quasi-SMILES is a sequence of special symbols-codes that reflect molecular features and codes of experimental conditions. SMILES and quasi-SMILES serve as a basis to develop QSPR/QSAR as well Nano-QSPR/QSAR via the Monte Carlo calculation that provides the so-called optimal descriptors for QSPR/QSAR models. The book presents a reliable technology for developing Nano-QSPR/QSAR while it also includes the description of the algorithms of the Monte Carlo optimization. It discusses the theory and practice of the technique of variational authodecoders (VAEs) based on SMILES and analyses in detail the index of ideality of correlation (IIC) and the correlation intensity index (CII) which are new criteria for the predictive potential of the model. The mathematical apparatus used is simple so that students of relevant specializations can easily follow. This volume is a valuable contribution to the field and will be of great interest to developers of models of physicochemical properties and biological activity, chemical technologists, and toxicologists involved in the area of drug design.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

This book analyzes the generation of the arrow-categories of a given category, which is a foundational and distinguishable Category Theory phenomena, in analogy to the foundational role of sets in the traditional set-based Mathematics, for defi nition of natural numbers as well. This inductive transformation of a category into the infinite hierarchy of the arrowcategories is extended to the functors and natural transformations. The author considers invariant categorial properties (the symmetries) under such inductive transformations. The book focuses in particular on Global symmetry (invariance of adjunctions) and Internal symmetries between arrows and objects in a category (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Internal symmetry to Computer Science: for Intuitionistic Logic, Untyped Lambda Calculus with Fixpoint Operators, Labeled Transition Systems in Process Algebras and Modal logics as well as Data Integration Theory.

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a ¿mathematical model checker¿ by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material.

Modeling and Control of Dynamic Spatially Distributed Systems: Pharmaceutical Processes provides a balanced approach to help readers to get started quickly in the field of biochemical pharmaceuticals. From a theoretical perspective, dynamic spatially distributed systems are introduced to address their industrial applications. After identifying problems, the book provides readers with modeling and control system design techniques via a novel fuzzy set (class of objects with a continuum of grades of membership, to describe the grade of the object belonging to this fuzzy set) and intelligent computation methods. From an application perspective, the book provides a thorough understanding of Good Manufacture Practices (GMP) and the importance of identification, modelling, and intelligent control of such systems, reducing the test-and-error cost, and the R&D design time cycle of original drug development.

Some of the hottest topics today involve cryptocurrency, and FinTech. With all these trends, businesses need to become better informed. This book provides an easy-to-read, yet comprehensive, view of cryptocurrency in the U.S. and international markets, as well as the key issues, technologies, applications, challenges, and trends.

Whether the source is more industry-based or academic research, there certainly appears to be a growing interest in the field of cryptocurrency. The New York Times had a cover story on March 24, 2022, titled "Time to Enter the Crypto Zone?," and they talked about institutional investors pouring billions into digital tokens, salaries being taken in Bitcoins, and even Bitcoin ATMs in grocery stores. Certainly, there have been ups and downs in crypto, but it has a kind of alluring presence that tempts one to include crypto as part of one's portfolio. Those who are "prime crypto-curious" investors are usually familiar with the tech/pop culture and feel they want to diversify a bit in this fast-moving market. Even universities are beginning to offer more courses and create "Centers on Cryptocurrency." Some universities are even requiring their students who take a crypto course to pay the course tuition via cryptocurrency.In response to the growing interest and fascination about the crypto industry and cryptocurrency in general, Cryptocurrency Concepts, Technology, and Applications brings together many leading worldwide contributors to discuss a broad range of issues associated with cryptocurrency. The book covers a wide array of crypto-related topics, including:BlockchainNFTsData analytics and AICrypto crimeCrypto industry and regulationCrypto and public choiceConsumer confidenceBitcoin and other cryptocurrencies.Presenting various viewpoints on where the crypto industry is heading, this timely book points out both the advantages and limitations of this emerging field. It is an easy-to-read, yet comprehensive, overview of cryptocurrency in the U.S. and international markets.

¿This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics¿despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist¿and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer¿s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its ¿existence¿ in an independent platonic realm, as Gödel believed.The book aims at readers interested in the history and philosophy of physics. It is accessible to those with only a very basic (not professional) knowledge of physics.

CoPart 3 is a dual complement to Visual Category Theory Brick by Brick Part 3. It covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks, pushouts.

This book helps readers easily learn basic model checking by presenting examples, exercises and case studies. The toolset mCRL2 provides a language to specify the behaviour of distributed systems, in particular where there is concurrency with inter-process communication. This language allows us to analyse a distributed system with respect to its functional requirements. For example, biological cells, supply chain management systems, patient support platforms, and communication protocols.The underlying technique is based on verifying requirements through model checking. The book explains the syntax of mCRL2 and offers modelling tips and tricks.

A set in mathematics is just a collection of elements; an example is the set of natural numbers {1, 2, 3, ...}. Simplifying somewhat, the theory of sets can be regarded as the foundation on which the whole of mathematics is built; and the founder of set theory is the German logician and mathematician Georg Cantor (1845¿1918). However, the aspect of Cantor's work that's most widely known-or most controversial, at any rate-isn't so much set theory in general, but rather those parts of that theory that have to do with infinite sets in particular. Cantor claimed among other things that the infinite set of real numbers contains strictly more elements than the infinite set of natural numbers. From this result, he concluded that there's more than one kind of infinity; in fact, he claimed that there are an infinite number of different infinities, or transfinite numbers. (He also believed these results had been communicated to him by God.) The aim of this book is to explain and investigate these claims of Cantor's in depth (and question them, where appropriate). It's not a textbook, though; instead, it's a popular account-it tells a story-and the target audience is interested lay readers, not mathematicians or logicians. What little mathematics is needed to understand the story is explained in the book itself.

Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the Third Tsinghua Interdisciplinary Workshop on Logic, Language, and Meaning, TLLM 2022, which was held virtually in April 2022.The 9 full papers presented in this volume were carefully reviewed and selected from 13 submissions. The workshop covers a wide range of topics such as dynamic semantics, logical dynamics, Dynamic Epistemic Logic, Discourse Representation Theory, formal semantics, free choice inference, update semantics, and donkey sentences.

This monograph is a defence of the Fregean take on logic. The author argues that Frege¿s projects, in logic and philosophy of language, are essentially connected and that the formalist shift produced by the work of Peano, Boole and Schroeder and continued by Hilbert and Tarski is completely alien to Frege's approach in the Begriffsschrift. A central thesis of the book is that judgeable contents, i.e. propositions, are the primary bearers of logical properties, which makes logic embedded in our conceptual system. This approach allows coherent and correct definitions of logical constants, logical consequence, and truth and connects their use to the practices of rational agents in science and everyday life.

This book constitutes the proceedings of the 5th International Workshop on Formal Methods Teaching, FMTea 2023, which was held in Lübeck, Germany, in March 2023.The 7 full papers presented in this volume were carefully reviewed and selected from 10 submissions. FMTea 2023 aim is to support a worldwide improvement in learning Formal Methods, mainly by teaching but also via self-learning.

Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023.Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.

This book constitutes revised selected papers from the refereed proceedings of the 4th International Workshop on Dynamic Logic, DaLí 2022, held in Haifa, Israel, in July/August 2022.The 8 full papers presented in this volume were carefully reviewed and selected from 22 submissions. They deal with new trends and applications in the area of Dynamic Logic.

This book is for readers who have learned about first order logic; Gödel's completeness theorem; the Löwenheim-Skolem theorem; the Tarski-Vaught criterion for being elementary sub-model; and who know naive set theory. A graduate course in model theory will be helpful. The thesis of the book is that we can find worthwhile dividing lines among complete first order theories T; mainly countable. That is, properties dividing them in some sense between understandable and complicated ones.The main test problem is the number of models of T of the infinite cardinal l as a function of l. This culminates in the so-called main gap theorem saying the number is either maximal or quite small in suitable sense. Toward this, other properties are introduced and investigated, such as being stable or being super stable, where can we define dimension and weight, particularly for super stable theories.

The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.

Paradoxes seized the attention of logicians in the middle ages, and were used both as tests for the viability of theories of logic, language, epistemology, and possibly every philosophical issue, and also in the specific genre of insolubles as needing a theoretical solution, usually involving issues about signification, truth, knowledge and modality. Numerous theories were developed, not only in the Latin West, but also in the Islamic world and in the Byzantine tradition. Some of these theories are well known, others barely investigated, if at all. The papers in this volume discuss and contrast a range of these theories and consider their advantages and drawbacks, and their relation to more recent theories of paradox and antinomy. Several of the papers were presented at a workshop organised at the University of St Andrews, Scotland, as part of the Leverhulme-funded project 'Theories of Paradox in Fourteenth-Century Logic: Edition and Translation of Key Texts'.