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Classical First-Order Logic

Classical First-Order Logic
Author: Stewart Shapiro
Publisher: Cambridge University Press
Total Pages: 89
Release: 2022-05-19
Genre: Philosophy
ISBN: 1108991521

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One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.


Extensions of First-Order Logic

Extensions of First-Order Logic
Author: Maria Manzano
Publisher: Cambridge University Press
Total Pages: 414
Release: 1996-03-29
Genre: Computers
ISBN: 9780521354356

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An introduction to many-sorted logic as an extension of first-order logic.


First-Order Logic and Automated Theorem Proving

First-Order Logic and Automated Theorem Proving
Author: Melvin Fitting
Publisher: Springer Science & Business Media
Total Pages: 258
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468403575

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There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scientists. Although there is a common core to all such books they will be very dif ferent in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer sci ence formal logic turns up in a number of areas, from program verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theorem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but not incompleteness issues. The first item to be addressed is, what are we talking about and why are we interested in it. We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self-evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject.


First-Order Logic

First-Order Logic
Author: John Heil
Publisher: Hackett Publishing
Total Pages: 303
Release: 2021-10-06
Genre: Philosophy
ISBN: 1647920108

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"In his introduction to this most welcome republication (and second edition) of his logic text, Heil clarifies his aim in writing and revising this book: 'I believe that anyone unfamiliar with the subject who set out to learn formal logic could do so relying solely on [this] book. That, in any case, is what I set out to create in writing An Introduction to First-Order Logic.' Heil has certainly accomplished this with perhaps the most explanatorily thorough and pedagogically rich text I’ve personally come across. "Heil's text stands out as being remarkably careful in its presentation and illuminating in its explanations—especially given its relatively short length when compared to the average logic textbook. It hits all of the necessary material that must be covered in an introductory deductive logic course, and then some. It also takes occasional excursions into side topics, successfully whetting the reader’s appetite for more advanced studies in logic. "The book is clearly written by an expert who has put in the effort for his readers, bothering at every step to see the point and then explain it clearly to his readers. Heil has found some very clever, original ways to introduce, motivate, and otherwise teach this material. The author's own special expertise and perspective—especially when it comes to tying philosophy of mind, linguistics, and philosophy of language into the lessons of logic—make for a creative and fresh take on basic logic. With its unique presentation and illuminating explanations, this book comes about as close as a text can come to imitating the learning environment of an actual classroom. Indeed, working through its presentations carefully, the reader feels as though he or she has just attended an illuminating lecture on the relevant topics!" —Jonah Schupbach, University of Utah


A Concise Introduction to Logic

A Concise Introduction to Logic
Author: Craig DeLancey
Publisher: Open SUNY Textbooks
Total Pages:
Release: 2017-02-06
Genre:
ISBN: 9781942341437

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Logic and Implication

Logic and Implication
Author: Petr Cintula
Publisher: Springer Nature
Total Pages: 465
Release: 2022-01-01
Genre: Philosophy
ISBN: 3030856755

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This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.


The Classical Decision Problem

The Classical Decision Problem
Author: Egon Börger
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2001-08-28
Genre: Mathematics
ISBN: 9783540423249

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This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.


Logical Options

Logical Options
Author: John L. Bell
Publisher: Broadview Press
Total Pages: 313
Release: 2001-03-30
Genre: Philosophy
ISBN: 1551112973

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Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.


First-Order Dynamic Logic

First-Order Dynamic Logic
Author: D. Harel
Publisher:
Total Pages: 152
Release: 2014-01-15
Genre:
ISBN: 9783662174500

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Principia Mathematica

Principia Mathematica
Author: Alfred North Whitehead
Publisher:
Total Pages: 688
Release: 1910
Genre: Logic, Symbolic and mathematical
ISBN:

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