Logical Options

An Introduction to Classical and Alternative Logics

John L. Bell, David Devidi, Graham Solomon (Autoren)

Buch | Softcover

312 Seiten

2001
Broadview Press Ltd (Verlag)
978-1-55111-297-8 (ISBN)

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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.

John L. Bell and David DeVidi are members of the Departments of Philosophy at the University of Western Ontario and the University of Waterloo, respectively. The late Graham Solomon was a member of the Department of Philosophy at Wilfrid Laurier University.

Preface

1 Classical Propositional Logic

Introductory Remarks

Some Basic Concepts
Formal Logics

Propositional Logic

Preliminaries
Truth Values, Valuations, and validity
Implication, Tautology, and Other Important Concepts
Equivalence and Expressive Completeness
Arithmetical Representation of Statements and Logical Operations

Trees for Classical Propositional Logic

Tree Rules for Classical Propositional Logic
Trees as a Test for Validity
Further Applications of the Tree Method

Metatheorems
Other Proof Methods

Classical Propositional Calculus
Natural Deduction
Sequent Calculus

2 Classical Predicate Logic

Introductory Remarks
Tree Rules for Classical Predicate Logic

Rules for Quantifiers
Identity
Functions

Predicate Languages and Their Interpretations

The Languages
Interpretations: Preliminary Remarks

Set Theory

Sets
Relations
Equivalence Relations
Orderings
Functions

Interpretations of Languages for Predicate Logic
Validity, Satisfiability, and Models
Correctness and Adequacy

Some Difficulties
Dealing with Difficulties
The Proofs

3 Using and Extending
Predicate Logic: Postulates, Sorts and Second-Order Logic

Postulate Systems

Postulate Systems for Arithmetic
Noncategoricity of First-Order Peano Arithmetic

Many Sorted Logic

Introductory Remarks
Many Sorted Languages and Interpretations
Reducing Many Sorted to Unsorted Logic

Second-Order Logic

Languages and Interpretations
Second-Order Trees
The Strength of Second-Order Logic
Metatheory of Second-Order Logic

4 Introducing Contextual Operators: Modal Logics

The Propositional Modal Language and Models

The Language
Interpretations
Classes of Frames and Different Logics

Trees for Contextual Logics

Proving Correctness for ▪
Counterexamples
Proving Adequacy for ▪

Other Systems of Contextual (Modal) Logic

Correctness and Adequacy for Trees

Provability Logic

Arithmetic Provability and Contextual Logic
Frames and Provability Logic
Trees for Provability Logic

Multi-Modal Logic
Quantificational Contextual Logic

The Languages
Introduction
Semantics for Contextual Predicate Logic
Concluding Remarks

5 Getting Away From Bivalence: Three-Valued and Intuitionistic Logic

Three-Valued Logics

Trees for Three-Valued Logic

Intuitionistic Logic

Introduction – Constructivism
A More General Account
Semantics and Countermodels
Metatheorems for Intuitionistic Propositional Logic
Comparing Intutionistic Logic to Other Logics

Intuitionistic Predicate Logic

Interpretations
Trees for Intuitionistic Predicate Logic
Intuitionistic Identity

6 A Sampling of Other Logics

Fuzzy Logic
Algebraic Logic
Term Forming Operators and Free Logics

Term Forming Operators
Free Logics

7 Solutions to *-ed Exercises

Solutions for Chapter 1
Solutions for Chapter 2
Solutions for Chapter 3
Solutions for Chapter 4
Solutions for Chapter 5
Solutions for Chapter 6

Index

Erscheint lt. Verlag	30.3.2001
Sprache	englisch
Maße	165 x 229 mm
Gewicht	458 g
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
ISBN-10	1-55111-297-3 / 1551112973
ISBN-13	978-1-55111-297-8 / 9781551112978
Zustand	Neuware