Formal Logic

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Formal Logic

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Author : Arthur N. Prior
language : en
Publisher:
Release Date : 1955

Formal Logic written by Arthur N. Prior and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with Logic categories.

Formal Logic

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Author : Richard Jeffrey
language : en
Publisher: Hackett Publishing
Release Date : 2006-03-15

Formal Logic written by Richard Jeffrey and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-15 with Philosophy categories.

The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic’s coming of age in the 20th century: Godel’s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification—once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs.

Formal Logic

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Author : Paul Hoyningen-Huene
language : en
Publisher: University of Pittsburgh Pre
Release Date : 2004-08-15

Formal Logic written by Paul Hoyningen-Huene and has been published by University of Pittsburgh Pre this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-15 with Philosophy categories.

Many texts on logic are written with a mathematical emphasis, and focus primarily on the development of a formal apparatus and associated techniques. In other, more philosophical texts, the topic is often presented as an indulgent collection of musings on issues for which technical solutions have long since been devised.What has been missing until now is an attempt to unite the motives underlying both approaches. Paul Hoyningen-Huene's Formal Logic seeks to find a balance between the necessity of formal considerations and the importance of full reflection and explanation about the seemingly arbitrary steps that occasionally confound even the most serious student of logic. Alex Levine's artful translation conveys both the content and style of the German edition. Filled with examples, exercises, and a straightforward look at some of the most common problems in teaching the subject, this work is eminently suitable for the classroom.

An Introduction To Formal Logic

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Author : Peter Smith
language : en
Publisher: Cambridge University Press
Release Date : 2003-11-06

An Introduction To Formal Logic written by Peter Smith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-11-06 with Mathematics categories.

Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.

Outlines Of Formal Logic

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Author : John of Saint Thomas
language : en
Publisher:
Release Date : 1962

Outlines Of Formal Logic written by John of Saint Thomas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Logic categories.

Proof And Disproof In Formal Logic

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Author : Richard Bornat
language : en
Publisher: OUP Oxford
Release Date : 2005-07-21

Proof And Disproof In Formal Logic written by Richard Bornat and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-21 with Mathematics categories.

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. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system--a collection of rules and axioms which define a universe of logical proofs--is what gives us programming languages and modern-day programming. 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 small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: · Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. · Part II "Formal syntactic proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. · Part III "Formal semantic disproof" shows you how to construct mathematical counterexamples to show that proof is impossible. Jape can check the counterexamples you build. · Part IV "Program specification and proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.

Reasoning And Formal Logic

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Author : Richard L Epstein
language : en
Publisher: Advanced Reasoning Forum
Release Date : 2018-11-05

Reasoning And Formal Logic written by Richard L Epstein and has been published by Advanced Reasoning Forum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Philosophy categories.

This series of books presents the fundamentals of logic in a style accessible to both students and scholars. The text of each essay presents a story, the main line of development of the ideas, while the notes and appendices place the research within a larger scholarly context. The basic theme here is the analysis of formal logic in terms of what metaphysical assumptions we need when we develop the formal systems we use. The essays together give a perspective of formal logic as part of the art of reasoning well. The essays are • Possibilities and Valid Inferences, • A General Framework for Semantics for Propositional Logics, • Why Are There So Many Logics? • Truth and Reasoning, • On Translations, • Reflections on Temporal and Modal Logic, • The Timelessness of Classical Predicate Logic, • Events in the Metaphysics of Predicate Logic, • Categoricity with Minimal Metaphysics, • Reflections on Gödel's Theorems, • On the Error in Frege's Proof that Names Denote, and • Postscript: Logic as the Art of Reasoning Well.

A History Of Formal Logic

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Author : Joseph M. Bochenski
language : en
Publisher: New York : Chelsea Publishing Company
Release Date : 1970

A History Of Formal Logic written by Joseph M. Bochenski and has been published by New York : Chelsea Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Philosophy categories.

Systems Of Formal Logic

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Author : L.H. Hackstaff
language : en
Publisher: Springer Science & Business Media
Release Date : 1966-07-31

Systems Of Formal Logic written by L.H. Hackstaff 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 1966-07-31 with Philosophy categories.

The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.

Formal Logic

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Author : P. Lorenzen
language : en
Publisher: Taylor & Francis
Release Date : 1965

Formal Logic written by P. Lorenzen and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Mathematics categories.

"Logic", one of the central words in Western intellectual history, compre hends in its meaning such diverse things as the Aristotelian syllogistic, the scholastic art of disputation, the transcendental logic of the Kantian critique, the dialectical logic of Hegel, and the mathematical logic of the Principia Mathematica of Whitehead and Russell. The term "Formal Logic", following Kant is generally used to distinguish formal logical reasonings, precisely as formal, from the remaining universal truths based on reason. (Cf. SCHOLZ, 1931). A text-book example of a formal-logical inference which from "Some men are philosophers" and "All philosophers are wise" concludes that "Some men are wise" is called formal, because the validity of this inference depends only on the form ofthe given sentences -in particular it does not depend on the truth or falsity of these sentences. (On the dependence of logic on natural language, English, for example, compare Section 1 and 8). The form of a sentence like "Some men are philosophers", is that which remains preserved when the given predicates, here "men" and "philosophers" are replaced by arbitrary ones. The form itself can thus be represented by replacing the given predicates by variables. Variables are signs devoid of meaning, which may serve merely to indicate the place where meaningful constants (here the predicates) are to be inserted. As variables we shall use - as did Aristotle - letters, say P, Q and R, as variables for predicates.