Deduction. Introductory Symbolic Logic

Deduction is a presentation of classical first-order logic. It presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague. Both are very natural and easy to learn. The definition of a formula excludes free variables, and the deduction system uses show lines; the combination allows rules to be stated very simply. The final part contains chapters on extensions and revisions of classical logic: modal logic, many-valued logic, fuzzy logic, intuitionistic logic, counterfactuals, deontic logic, common sense reasoning and quantified modal logic. These have been areas of great logical and philosophical interest since the 1960s. The book aims to make these areas accessible to introductory students. All chapters have discussions of the underlying semantics and present both truth tree and deduction systems.New features in this edition, in addition to truth tree systems for classical and nonclassical logics, include new and simpler rules for modal logic, deontic logic and counterfactuals; discussions of many-valued, fuzzy, and intuitionistic logics; an introduction to common sense reasoning (nonmonotonic logic); and extensively reworked problem sets, designed to lead students gradually from easier to more difficult problems. This edition also features web-based programs which make use of the book´s methods. Each program is set up to give students symbolization problems, give them hints, grade their work and do problems for them.
Contents: 1. Basic Concepts Of Logic: Arguments. Validity. Implication And Equivalence. Logical Properties Of Sentences. Satisfiability. 2. Sentences: The Language Of Sentential Logic. Truth Functions. A Sentential Language. Symbolization. Validity. Truth Tables. Truth Tables For Formulas. Truth Tables For Argument Forms. Implication, Equivalence And Satisfiability. 3. Truth Trees: Thinking Backwards. Constructing Truth Trees. Negation, Conjunction, And Disjunction. The Conditional And Biconditional. Other Applications. 4. Natural Deduction: Natural Deduction Systems. Rules For Negation And Conjunction. Rules For The Conditional And Biconditional. Rules For Disjunction. Derivable Rules. 5. Quantifiers: Constants And Quantifiers. Categorical Sentence Forms. Polyadic Predicates. The Language Q. Symbolization. 6. Quantified Truth Trees: Rules For Quantifiers. Strategies. Interpretations. Constructing Interpretations From Trees. 7. Quantified Natural Deduction: Deduction Rules For Quantifiers. Universal Proof. Derived Rules For Quantifiers. 8. Identity And Function Symbols: Identity. Truth Tree Rules For Identity. Deduction Rules For Identity. Function Symbols. 9. Necessity: If. Modal Connectives. Symbolization. Modal Truth Trees. Other Tree Rules. World Travelling. Modal Deduction. Other Modal Systems. 10. Between Truth And Falsehood: Vagueness And Presupposition. Many-Valued Truth Tables. Many-Valued Trees. Many-Valued Deduction. Fuzzy Logic. Intuitionistic Logic. 11. Obligation: Deontic Connectives. Deontic Truth Trees. Deontic Deduction. Moral And Practical Reasoning. 12. Counterfactuals: The Meaning Of Counterfactuals. Truth Tree Rules For Counterfactuals. Deduction Rules For Counterfactuals. Stalnaker´s Semantics. Lewis´s Semantics. 13. Common Sense Reasoning: When Good Arguments Go Bad. Truth Trees. Defeasible Deduction. Defeasible Deontic Logic. 14. Quantifiers And Modality: Quantified S5. Free Logic.