Logical Methods
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Logical Methods
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Author : John N. Crossley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Logical Methods written by John N. Crossley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics.
Logical Methods
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Author : Greg Restall
language : en
Publisher: MIT Press
Release Date : 2023-01-03
Logical Methods written by Greg Restall and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-03 with Philosophy categories.
An accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed. Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy. This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs. Features: An accessible introduction to proof theory for readers with no background in logic Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics Provides tools and techniques of particular interest to philosophers and philosophical logicians Features short summaries of key concepts and skills at the end of each chapter Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions
Logical Methods
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Author : Roger Antonsen
language : en
Publisher: Springer
Release Date : 2021-02-11
Logical Methods written by Roger Antonsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-11 with Computers categories.
Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.
Complicated Methods Of Logical Analysis Based On Simple Mathematics
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Author : Boris Kulik
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-03-10
Complicated Methods Of Logical Analysis Based On Simple Mathematics written by Boris Kulik and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Psychology categories.
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.
Linguistic Fuzzy Logic Methods In Social Sciences
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Author : Badredine Arfi
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-06-17
Linguistic Fuzzy Logic Methods In Social Sciences written by Badredine Arfi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-17 with Computers categories.
The book, titled “Linguistic Fuzzy-Logic Methods in Social Sciences,” is a first in its kind. Linguistic fuzzy logic theory deals with sets or categories whose boundaries are blurry or, in other words, “fuzzy,” and which are expressed in a formalism that uses “words” to compute, not numbers, termed in engineering as “soft computing.” This book presents an accessible introduction to this linguistic fuzzy logic methodology, focusing on its applicability to social sciences. Specifically, this is the first book to propose an approach based on linguistic fuzzy-logic and the method of computing with words to the analysis of decision making processes, strategic interactions, causality, and data analysis in social sciences. The project consists of systematic, theoretical and practical discussions and developments of these new methods as well as their applications to various substantive issues of interest to international relations scholars, political scientists, and social scientists in general.
Wittgenstein On Logic As The Method Of Philosophy
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Author : Oskari Kuusela
language : en
Publisher: Oxford University Press
Release Date : 2019-01-03
Wittgenstein On Logic As The Method Of Philosophy written by Oskari Kuusela and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-03 with Philosophy categories.
In Wittgenstein on Logic as the Method of Philosophy, Oskari Kuusela examines Wittgenstein's early and late philosophies of logic, situating their philosophical significance in early and middle analytic philosophy with particular reference to Frege, Russell, Carnap, and Strawson. He argues that not only the early but also the later Wittgenstein sought to further develop the logical-philosophical approaches of his contemporaries. Throughout his career Wittgenstein's aim was to resolve problems with and address the limitations of Frege's and Russell's accounts of logic and their logical methodologies so as to achieve the philosophical progress that originally motivated the logical-philosophical approach. By re-examining the roots and development of analytic philosophy, Kuusela seeks to open up covered up paths for the further development of analytic philosophy. Offering a novel interpretation of the philosopher, he explains how Wittgenstein extends logical methodology beyond calculus-based logical methods and how his novel account of the status of logic enables one to do justice to the complexity and richness of language use and thought while retaining rigour and ideals of logic such as simplicity and exactness. In addition, this volume outlines the new kind of non-empiricist naturalism developed in Wittgenstein's later work and explaining how his account of logic can be used to dissolve the long-standing methodological dispute between the ideal and ordinary language schools of analytic philosophy. It is of interest to scholars, researchers, and advance students of philosophy interested in engaging with a number of scholarly debates.
Optimization Methods For Logical Inference
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Author : Vijay Chandru
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-26
Optimization Methods For Logical Inference written by Vijay Chandru and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-26 with Mathematics categories.
Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks. . . it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering.
Algebraic Methods Of Mathematical Logic
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Author : Ladislav Rieger
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Algebraic Methods Of Mathematical Logic written by Ladislav Rieger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-mathematical parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semantic rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.
Galen S Method Of Healing
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Author : Richard Durling
language : en
Publisher: BRILL
Release Date : 2018-07-17
Galen S Method Of Healing written by Richard Durling and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-17 with History categories.
This book includes papers presented in Kiel in 1982 on Galen's chief therapeutic manual, the Methodus medendi. The papers describe the composition of the book, its surgical content, its emphasis on logic, and its fortuna in medieval Islam and Renaissance Europe. No such study in depth of a major Galenic work has hitherto been attempted.