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Logic, Symbolic and mathematical

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Algebraic logic. --- Logic, Symbolic and mathematical

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Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.

Logic, Symbolic and mathematical --- Paradox --- Dialetheism --- Inconsistency (Logic) --- Dialetheism. --- Logic, Symbolic and mathematical. --- Paradox.

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Build production-ready machine learning and NLP systems using functional programming, development platforms, and cloud deployment. KEY FEATURES ● In-depth explanation and code samples highlighting the features of the Julia language. ● Extensive coverage of the Julia development ecosystem, package management, DevOps environment integration, and performance management tools. ● Exposure to the most important Julia packages that aid in Data and Text Analytics and Deep Learning. DESCRIPTION The Julia Programming language enables data scientists and programmers to create prototypes without sacrificing performance. Nonetheless, skeptics question its readiness for production deployments as a new platform with a 1.0 release in 2018. This book removes these doubts and offers a comprehensive glimpse at the language's use throughout developing and deploying production-ready applications. The first part of the book teaches experienced programmers and scientists about the Julia language features in great detail. The second part consists of gaining hands-on experience with the development environment, debugging, programming guidelines, package management, and cloud deployment strategies. In the final section, readers are introduced to a variety of third-party packages available in the Julia ecosystem for Data Processing, Text Analytics, and developing Deep Learning models. This book provides an extensive overview of the programming language and broadens understanding of the Julia ecosystem. As a result, it assists programmers, scientists, and information architects in selecting Julia for their next production deployments. WHAT YOU WILL LEARN ● Get to know the complete fundamentals of Julia programming. ● Explore Julia development frameworks and how to work with them. ● Dig deeper into the concepts and applications of functional programming. ● Uncover the Julia infrastructure for development, testing, and deployment. ● Learn to practice Julia libraries and the Julia package ecosystem. ● Processing Data, Deep Learning, and Natural Language Processing with Julia. WHO THIS BOOK IS FOR This book is for Data Scientists and application developers who want to learn about Julia application development. No prior Julia knowledge is required but knowing the basics of programming helps understand the objectives of this book. TABLE OF CONTENTS 1. Getting Started 2. Data Types 3. Conditions, Control Flow, and Iterations 4. Functions and Methods 5. Collections 6. Arrays 7. Strings 8. Metaprogramming 9. Standard Libraries Module 2. The Development Environment 10. Programming Guidelines in Julia 11. Performance Management 12. IDE and Debugging 13. Package Management 14. Deployment Module 3. Packages in Julia 15. Data Transformations 16. Text Analytics 17. Deep Learning.

Logic, Symbolic and mathematical. --- Big data. --- Computer programming.

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"Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail" [Publisher]

Proof theory. --- Logique informatique. --- Théorie de la démonstration. --- Logic, Symbolic and mathematical. --- Logique informatique --- Théorie de la démonstration --- Proof theory --- Logic, Symbolic and mathematical