Logical Options: An Introduction to Classical and Alternative Logics

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.

Table of Contents:
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

About the Author :
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.

Review :
“I love this book; I would have written it if I’d known how!” — Richard Jeffrey, Princeton University “Logic teachers will love this book. Trees are probably the most accessible way to present logical systems to students and Bell, DeVidi and Solomon give tree formulations of a wide range of central logical systems—including truth-functional and quantificational logic, modal logic, provability logic, intuitionistic logic, three-valued logic, and free logic.… An excellent job.” — B. Jack Copeland, University of Canterbury