The Solution of Equations in the Calculus of Logic PDF Download
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Author: Leopold Löwenheim
Publisher:
ISBN:
Category : Disjunction (Logic)
Languages : en
Pages : 88
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Book Description
This paper contains an analysis of methods of solving equations in the calculus of logic. The work of Korselt in this area is reviewed and expanded with derivation of all propositions from an original point of view. (Author)
Author: Leopold Löwenheim
Publisher:
ISBN:
Category : Disjunction (Logic)
Languages : en
Pages : 88
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Book Description
This paper contains an analysis of methods of solving equations in the calculus of logic. The work of Korselt in this area is reviewed and expanded with derivation of all propositions from an original point of view. (Author)
Author: George Boole
Publisher:
ISBN:
Category : Analysis (Philosophy).
Languages : en
Pages : 94
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Book Description
Author: George Boole
Publisher: Createspace Independent Publishing Platform
ISBN: 9781548204679
Category :
Languages : en
Pages : 90
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Book Description
George Boole, an English mathematician, philosopher, educator, and logician. Worked in the fields of algebraic logic and differential equations, and is best known as the author of The Laws of Thought (ISBN: 978-1548119911) that contains Boolean algebra. Boolean is credited with laying the foundations for the information age. Boole sustained that no general formula for the solution of questions in the theory of probabilities can be established that does not explicitly recognize, not only the numerical basis of the science. But also those accepted laws of thought which are the foundation of all reasoning, whatever they may be as to their nature, are at least mathematical as to their form. Boole earned the Keith Medal by the Royal Society of Edinburgh, was elected a Fellow of the Royal Society (FRS), and received honorary degrees of LL.D. from the University of Dublin and the University of Oxford.
Author: Louis Couturat
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 124
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Book Description
Author: Bernd Steinbach
Publisher: Springer Science & Business Media
ISBN: 1402095953
Category : Computers
Languages : en
Pages : 232
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Book Description
Tsutomu Sasao – Kyushu Institute of Technology, Japan The material covered in this book is quite unique especially for p- ple who are reading English, since such material is quite hard to ?nd in the U.S. literature. German and Russian people have independently developed their theories, but such work is not well known in the U.S. societies. On the other hand, the theories developed in the U.S. are not conveyed to the other places. Thus, the same theory is re-invented or re-discovered in various places. For example, the switching theory was developed independently in the U.S., Europe, and Japan, almost at the same time [4, 18, 19]. Thus, the same notions are represented by di?- ent terminologies. For example, the Shegalkin polynomial is often called complement-free ring-sum, Reed-Muller expression [10], or Positive - larityReed-Mullerexpression [19].Anyway,itisquitedesirablethatsuch a unique book like this is written in English, and many people can read it without any di?culties. The authors have developed a logic system called XBOOLE.Itp- forms logical operations on the given functions. With XBOOLE, the readers can solve the problems given in the book. Many examples and complete solutions to the problems are shown, so the readers can study at home. I believe that the book containing many exercises and their solutions [9] is quite useful not only for the students, but also the p- fessors.
Author: Louis Couturat
Publisher: BoD - Books on Demand
ISBN:
Category : Mathematics
Languages : en
Pages : 96
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Book Description
Louis Couturat (French: [kutyʁa]; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. He was the French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to The Principles of Mathematics by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic logic as a tool to advance both mathematics and the philosophy of mathematics. In this, he was opposed by Henri Poincaré, who took considerable exception to Couturat's efforts to interest the French in symbolic logic. With the benefit of hindsight, we can see that Couturat was in broad agreement with the logicism of Russell, while Poincaré anticipated Brouwer's intuitionism. His first major publication was Couturat (1896). In 1901, he published La Logique de Leibniz, a detailed study of Leibniz the logician, based on his examination of the huge Leibniz Nachlass in Hanover. Even though Leibniz had died in 1716, his Nachlass was cataloged only in 1895. Only then was it possible to determine the extent of Leibniz's unpublished work on logic. In 1903, Couturat published much of that work in another large volume, his Opuscules et Fragments Inedits de Leibniz, containing many of the documents he had examined while writing La Logique. Couturat was thus the first to appreciate that Leibniz was the greatest logician during the more than 2000 years that separate Aristotle from George Boole and Augustus De Morgan. A significant part of the 20th century Leibniz revival is grounded in Couturat's editorial and exegetical efforts. This work on Leibniz attracted Russell, also the author of a 1900 book on Leibniz, and thus began their professional correspondence and friendship. In 1905, Couturat published a work on logic and the foundations of mathematics (with an appendix on Kant's philosophy of mathematics) that was originally conceived as a translation of Russell's Principles of Mathematics. In the same year, he published L'Algèbre de la logique, a classic introduction to Boolean algebra and the works of C.S. Peirce and Ernst Schröder.
Author: Christian Posthoff
Publisher: Springer Science & Business Media
ISBN: 1402029381
Category : Mathematics
Languages : en
Pages : 410
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Book Description
Logic functions and equations are (some of) the most important concepts of Computer Science with many applications such as Binary Arithmetics, Coding, Complexity, Logic Design, Programming, Computer Architecture and Artificial Intelligence. They are very often studied in a minimum way prior to or together with their respective applications. Based on our long-time teaching experience, a comprehensive presentation of these concepts is given, especially emphasising a thorough understanding as well as numerical and computer-based solution methods. Any applications and examples from all the respective areas are given that can be dealt with in a unified way. They offer a broad understanding of the recent developments in Computer Science and are directly applicable in professional life. Logic Functions and Equations is highly recommended for a one- or two-semester course in many Computer Science or computer Science-oriented programmes. It allows students an easy high-level access to these methods and enables sophisticated applications in many different areas. It elegantly bridges the gap between Mathematics and the required theoretical foundations of Computer Science.
Author: George Boole
Publisher: Literary Licensing, LLC
ISBN: 9781498167291
Category :
Languages : en
Pages : 86
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Book Description
This Is A New Release Of The Original 1847 Edition.
Author: Christian Prehofer
Publisher: Springer Science & Business Media
ISBN: 1461217784
Category : Computers
Languages : en
Pages : 193
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Book Description
This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.
Author: George Boole
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 414
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Book Description
Written by the founder of symbolic logic (and Boolean algebra), this classic treatise on the calculus of finite differences offers a thorough discussion of the basic principles of the subject, covering nearly all the major theorems and methods with clarity and rigor. Includes more than 200 problems. 1872 edition.
