Language Proof And Logic Download Ebook PDF Epub Online

Author : Dave Barker-Plummer
Jon Barwise
Publisher : Stanford Univ Center for the Study
Release : 2011
Page : 606
Category : Computers
ISBN 13 : 9781575866321
Description :


Rev. ed. of: Language, proof, and logic / Jon Barwise & John Etchemendy.


Author : Jon Barwise
John Etchemendy
Publisher : Seven Bridges PressLlc
Release : 2000
Page : 587
Category : Philosophy
ISBN 13 :
Description :


Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs, and an Internet-based grading service.


Author : David W. Agler
Publisher : Rowman & Littlefield
Release : 2012-12-13
Page : 375
Category : Mathematics
ISBN 13 : 1442217421
Description :


Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs.


Author : Alfred Jules Ayer
Publisher : Courier Corporation
Release : 2012-04-18
Page : 160
Category : Philosophy
ISBN 13 : 0486113094
Description :


"A delightful book … I should like to have written it myself." — Bertrand Russell First published in 1936, this first full-length presentation in English of the Logical Positivism of Carnap, Neurath, and others has gone through many printings to become a classic of thought and communication. It not only surveys one of the most important areas of modern thought; it also shows the confusion that arises from imperfect understanding of the uses of language. A first-rate antidote for fuzzy thought and muddled writing, this remarkable book has helped philosophers, writers, speakers, teachers, students, and general readers alike. Mr. Ayers sets up specific tests by which you can easily evaluate statements of ideas. You will also learn how to distinguish ideas that cannot be verified by experience — those expressing religious, moral, or aesthetic experience, those expounding theological or metaphysical doctrine, and those dealing with a priori truth. The basic thesis of this work is that philosophy should not squander its energies upon the unknowable, but should perform its proper function in criticism and analysis.


Author : Nils Kürbis
Publisher : Cambridge University Press
Release : 2019-04-30
Page : 320
Category : Philosophy
ISBN 13 : 1108481302
Description :


This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Krbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech act of denial - and concludes that they cannot adequately do so. He argues that whereas proof-theoretic semantics usually only appeals to a notion of truth, it also needs to appeal to a notion of falsity, and proposes a system of natural deduction in which both are incorporated. Offering new perspectives on negation, denial and falsity, his book will be important for readers working on logic, metaphysics and the philosophy of language.


Author : Richard H. Hammack
Publisher :
Release : 2016-01-01
Page : 314
Category : Mathematics
ISBN 13 : 9780989472111
Description :


This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.


Author : Lawrence C. Paulson
Publisher : Cambridge University Press
Release : 1990-07-26
Page : 320
Category : Computers
ISBN 13 : 9780521395601
Description :


This book is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines the methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of program statements. Cambridge LCF is based on an earlier theorem-proving system, Edinburgh LCF, which introduced a design that gives the user flexibility to use and extend the system. A goal of this book is to explain the design, which has been adopted in several other systems. The book consists of two parts. Part I outlines the mathematical preliminaries, elementary logic and domain theory, and explains them at an intuitive level, giving reference to more advanced reading; Part II provides sufficient detail to serve as a reference manual for Cambridge LCF. It will also be a useful guide for implementors of other programs based on the LCF approach.


Author : Torben Braüner
Publisher : Springer Science & Business Media
Release : 2010-11-17
Page : 231
Category : Philosophy
ISBN 13 : 9789400700024
Description :


This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).


Author : Robert S. Wolf
Publisher : W. H. Freeman
Release : 1997-12-15
Page : 4
Category : Mathematics
ISBN 13 : 9780716730507
Description :


This text is designed to teach students how to read and write proofs in mathematics and to acquaint them with how mathematicians investigate problems and formulate conjecture.


Author : Daniel J. Velleman
Publisher : Cambridge University Press
Release : 2006-01-16
Page : 384
Category : Mathematics
ISBN 13 : 0521861241
Description :


Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.


Author : Howard Gregory
Publisher : Edinburgh University Press
Release : 2015-07-08
Page : 328
Category : Language Arts & Disciplines
ISBN 13 : 0748691650
Description :


Taking linguistics students beyond the classical forms often taught in introductory courses, Language and Logics offers a comprehensive introduction to the wide variety of useful non-classical logics that are commonly used in research. Including a brief review of classical logic and its major assumptions, this textbook provides a guided tour of modal, many valued and substructural logics. The textbook starts from simple and intuitive concepts, clearly explaining the logics of language for linguistics students who have little previous knowledge of logic or mathematics. Issues are presented and discussed clearly before going on to introduce symbolic notation.While not avoiding technical detail, the book focuses throughout on helping students develop an intuitive understanding of the field, with particular attention to conceptual questions and to the tailoring of logical systems to thinking about different applications in linguistics and beyond. This is an ideal introductory volume for advanced undergraduates and beginning postgraduate students in linguistics, and for those specializing in semantics.


Author : Alfred North Whitehead
Bertrand Russell
Publisher : Cambridge University Press
Release : 1997-09-11
Page : 410
Category : Mathematics
ISBN 13 : 0521626064
Description :


This abridged text of the most famous work ever written on the foundations of mathematics contains material that is most relevant to an introductory study of logic and the philosophy of mathematics.


Author : S.R. Buss
Publisher : Elsevier
Release : 1998-07-09
Page : 810
Category : Mathematics
ISBN 13 : 9780080533186
Description :


This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.


Author : Rob Nederpelt
Herman Geuvers
Publisher : Cambridge University Press
Release : 2014-11-06
Page : 490
Category : Computers
ISBN 13 : 110703650X
Description :


A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.


Author : J. L. Ackrill
Publisher : Princeton University Press
Release : 1988-01-01
Page : 600
Category : Philosophy
ISBN 13 : 1400835828
Description :


In a single volume that will be of service to philosophy students of all levels and to their teachers, this reader provides modern, accurate translations of the texts necessary for a careful study of most aspects of Aristotle's philosophy. In selecting the texts Professor J. L. Ackrill has drawn on his broad experience of teaching graduate classes, and his choice reflects issues of current philosophical interest as well as the perennial themes. Only recent translations which achieve a high level of accuracy have been chosen; the aim is to place the Greekless reader, as nearly as possible, in the position of a reader of Greek. As an aid to study, Professor Ackrill supplies a valuable guide to the key topics covered. The guide gives references to the works or passages contained in the reader, and indication of their interrelations, and current bibliography.


Author : Dave Barker-Plummer
Jon Barwise
Publisher : Lecture Notes
Release : 2017
Page : 210
Category : Language Arts & Disciplines
ISBN 13 : 9781575869513
Description :


The Hyperproof courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of a textbook, desktop applications and online materials. Unlike traditional formal treatments of reasoning, the Hyperproof approach uses both graphical and sentential representations of information. This reflects common situations in everyday reasoning which involve information expressed in many forms, such as finding your way to a location using a map and an address, or interpreting a newspaper story involving both text and a graphic. Using Hyperproof the student learns to construct proofs of both consequence and non-consequence using an intuitive proof system which extends standard treatments of proof with sentential, graphical and heterogeneous inference rules. The approach allows students to focus on the content of proofs, rather than on the syntactic structure of formal sentences. Proofs of consistency and inconsistency as well as independence proofs may also be constructed in the system. The desktop application can be used to check the logical validity of all of the different types of proof. The Hyperproof courseware package contains more than 300 exercises, of which more than 250 can assessed by the Grade Grinder online assessment service. The courseware is supported by an extensive web site through which students and instructors can access online video lectures by the authors. Instructors also have the ability to create their own exercises for assessment and access to assessments of the work submitted by their students. Hyperproof builds on the Tarski s World and Language, Proof and Logic courseware packages from the same authors. The material in these packages can be combined to create a variety of different courses, or incorporate as engaging components of courses that teach logical reasoning, including formal linguistics, philosophy, mathematics, and computer science. "


Author : Imre Lakatos
Lakatos Imre
Publisher : Cambridge University Press
Release : 1976
Page : 174
Category : Philosophy
ISBN 13 : 9780521290388
Description :


Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.


Author : Gerard Allwein
Jon Barwise
Publisher : Oxford University Press on Demand
Release : 1996
Page : 270
Category : Computers
ISBN 13 : 0195104277
Description :


The authors explore the logical properties of diagrams, charts, and maps, and the role these play in problem solving and teaching reasoning skills.


Author : Peter B. Andrews
Publisher : Springer Science & Business Media
Release : 2013-04-17
Page : 390
Category : Mathematics
ISBN 13 : 9401599343
Description :


In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.


Author : Richard Bornat
Publisher : Oxford University Press on Demand
Release : 2005
Page : 243
Category : Mathematics
ISBN 13 : 0198530277
Description :


Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses - natural deduction - is very simple and shows how large mathematical universes can be built on small foundations. Aimed at undergraduates and graduates in computerscience, logic, mathematics, and philosophy, the text includes reference to...