• Preface
• Acknowledgements
• Check your browser
• Complete list of exercises
• Introduction
• Chapter 1: Logic: The theory of deductive inference
1. Arguments
1. Deductive inference
2. Codifying real arguments
• Chapter 2: The Syntax of Propositional Logic (PL)
1. Propositions and connectives in natural language
1. Simple propositions
2. Complex propositions
3. Connectives and operators
2. The well-formed formulas (wffs) of PL
3. The main operator
4. Polish Notation (Extra Credit)
• Chapter 3: The Semantics of Propositional Logic (PL)
1. The Rules of Truth
2. Basic truth-tables
3. Determining truth and falsity of complex wffs
4. Constructing complete truth-tables
5. Truth-functional vs. non-truth-functional operators
6. Translation from English to PL
7. More on Translation
   1. Negation
   2. Conjunction
   3. Disjunction
   4. Conditional
   5. Biconditional
• Chapter 4: Validity and Other Semantic Properties
1. Semantic status of wffs
   1. tautologies
   2. contradictions
   3. contingencies
2. Logical equivalence
3. Consistency
4. Validity
• Chapter 5: More Efficient Semantic Methods
1. Gappy Truth Tables
2. Other Gappy Truth Table Tests
3. Truth Trees
   1. Theory and Practice of Truth Trees
   2. Application of the Truth Tree Method
   3. Truth-Tree Rules for Non-PL Operators
4. Decision Procedures
5. Truth-functional Completeness
6. The Sheffer Stroke (extra credit)
7. Summary of Semantic Methods
• Chapter 6: Proof Theory for Propositional Logic
  1. Proof and Truth
  2. Derivations
  3. Rules of Inference
  4. Constructing Derivations
  5. Proofs
  6. Examples and Strategies
  7. Equivalence Rules
  8. More Examples and Strategies
  9. Conditional Proof
  10. Indirect Proof
  11. Theorems
  12. Completeness and Consistency
• Chapter 7: Introduction to Quantificational Logic
1. Singular Propositions
2. Simple Quantified Propositions
3. Negations of Simple Quantified Propositions
4. Quantified Negations
5. Truth-Functional Propositions
6. Introduction to Categorical Propositions
• Chapter 8: Traditional Logic
  1. Categorical Propositions
  2. Recognizing Categorical Propositions in English
  3. The Semantics of Categorical Propositions
  4. The Square of Opposition
  5. The Traditional Square of Opposition
  6. The Revised Square of Opposition
  7. Syllogisms
  8. Testing Syllogisms for Validity using Venn Diagrams
  9. Testing Syllogisms for Validity using Truth-Trees
  10. Testing Syllogisms for Validity using Rules for Valid Syllogisms
• Chapter 9: Categorical Propositions in Quantificational Logic
  1. Universally Quantified Categorical Propositions
  2. Existentially Quantified Categorical Propositions
  3. Negations of Categorical Propositions
  4. Categorical Propositions with Complex Subjects and Predicates
  5. Putting it Together in QL
• Chapter 10: Semantics for Quantificational Logic
  1. QL vs. PL Semantics
  2. Semantic Properties in QL
  3. Constructing a Model Universe
  4. Truth-Trees for QL
  5. Examples of Truth-Trees in QL
  6. Truth-Trees and Model Universes
• Chapter 11: Proof Theory for Quantificational Logic
  1. Quantifier Negation Rules
  2. The Instantiation Rules
  3. The Generalization Rules
  4. Sample Proofs in QL
  5. How to Misapply QL Rules
• Chapter 12: Polyadic Quantificational Logic
  1. Introduction to Relations
  2. Mixed Quantification
  3. Translation in Polyadic QL
  4. Individuals, Properties and Relations
  5. Validity in Polyadic QL
  6. The Undecidibility of Polyadic QL
  7. Proofs in Polyadic QL
• Chapter 13: Identity
  1. Identity and Non-Identity Propositions
  2. Numerical Propositions
  3. Superlatives and Exceptives
  4. Definite Descriptions
  5. Properties of Relations
  6. Proofs in QL with Identity
• Appendices
  1. Inductive Inference
  2. Truth-Tree Rules for PL
  3. Rules of Inference for PL
  4. Equivalence Rules for PL
  5. Rules for Valid Syllogisms
  6. Quantifier Negation Rules for QL
  7. Instantiation and Generalization Rules for QL
  8. Identity Rules for QL
     

 Last updated: 02/25/18