Elements of Deductive Inference An Introduction to Symbolic Logic

ISBN-10: 0534551211
ISBN-13: 9780534551216
Edition: 2000
List price: $200.95
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Description: The text covers elementary logic, from statement logic through relational logic with identity and function symbols. The authors acquaint students with formal techniques at a level appropriate for undergraduates, but extends far enough and deep  More...

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Book details

List price: $200.95
Copyright year: 2000
Publisher: Wadsworth
Publication date: 8/2/1999
Binding: Mixed Media
Pages: 344
Size: 6.50" wide x 10.00" long x 1.00" tall
Weight: 1.782
Language: English

The text covers elementary logic, from statement logic through relational logic with identity and function symbols. The authors acquaint students with formal techniques at a level appropriate for undergraduates, but extends far enough and deep enough into the subject that it is suitable for a brief first-year graduate course. The text covers full and brief truth tables, and presents the method of truth (consistency) trees and natural deduction for the whole of elementary logic. The text's organization allows instructors to cover just statement logic, or statement logic combined with various extensions into predicate logic: monadic logic with or without identity, or the preceding plus relational logic with or without identity and with or without function symbols. At each stage, the instructor may elect to pursue truth trees and/or natural deduction. A final chapter provides a perspective for further study and applications of logic. The text may be used with or without the accompanying software.

Editor''s Preface
Acknowledgments
Introduction
Logic and Argument
Deduction and Induction
Statements, Propositions, and Context
Use and Mention
Statement Logic I: A New Language
Introduction
Truth-Functionally Compound Statements
Symbolizing Simple and Compound Statements
Symbolizing More Complex Statements and Arguments
Spelling It Out Formally
Statement Logic Ii: Semantic Methods
Introduction
Truth Tables
Formalized Semantics for SL
Truth-Functional Validity and Tautologousness
Further Semantic Properties and Relationships
Truth-Functional Consistency
The Material Conditional Revisited
Brief Truth Tables
Truth Trees
Using Truth Trees to Test for Other Semantic Properties
The Adequacy of the Tree Method
statement logic iii: syntactic methods
Introduction
Whole Line Inference Rules for DSL
Replacement Rules for DSL
Conditional Proof and Reduction ad Absurdum
Proof Strategy
Proving Tautologousness and Other Semantic Properties
The Adequacy of the Natural Deduction System DSL
Additional Inference Rules
A Second Look at the Truth Table for the Material Conditional
Predicate Logic I: Syntax And Semantics
Introduction
Informal Introduction to the Language of Predicate Logic
Syntax for L
Formal Semantics I: Interpretations
Formal Semantics II: Truth Under an Interpretation
Symbolizing English I: Monadic Logic and Categorical Forms
Symbolizing English II: Polyadic Logic and Nested Quantifiers
Semantic Properties and Relationships for L
Classifying Logical Relations
Predicate Logic Ii: Semantic Methods
Introduction
Truth Trees
Reading Interpretations From Finished Open Paths
The Problem of Infinite Trees
The Adequacy of the Tree Method for Lm and L
Soundness, Completeness, and Undecidability
Monadic Predicate Logic Iii: Syntactic Methods
Introduction
The Rules UI, EG, and Q
The Rules UG, R, PA-EI and EI
The Adequacy of DL
Extensions To L: Identity, Relations And Functions
Introduction
Syntax and Semantics for L
Symbolization in L= I: ''At Least'', ''At Most'', and ''Exactly''
Symbolization in L= II: Identity and Polyadic Predicates
Truth Trees for L
Natural Deduction in L
Syntax and Semantics for L
Symbolization in L
Truth Trees in L
Natural Deduction in L
Some Applications And Limitations Of L
Introduction
Definite Descriptions and Ontological Commitment
Axiom Systems for Arithmetic
The Incompleteness of Arithmetic
Applications of Axiomatic Theories to the Philosophy of Science
Higher Order Logic
Modal Logic
Strict and Counterfactual Conditionals
General Intensional Logic
Deontic Logic
Free Logic
Many-Valued Logic
Further Reading in Logic
Answer to Selected Exercises
Index

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