Lecture: Proof Tactics, Strategies and Derived Rules

Background Material

• Natural Deduction
• Proof by Contradiction
• Proofs encountered in various math courses.

Reading

• Chapter 5 of CMU OLI text.

Topics

• Review rules of natural deduction and their forward and backward application.
• Positive subformulas and extraction
• Proof tactics
  1. Extraction
  2. Conversion
  3. Inversion
  4. Division
  5. Refutation
• Finding contradictions
• Proof strategies and an algorithm to find a proof
• Derived rules
  1. Commutivity
  2. Associativity
  3. Idempotence
  4. Distributivity
  5. Cut and resolution
  6. DeMorgan's laws
  7. Modus tollens
  8. Transposition
  9. Hypothetical syllogism
  10. Exportation and Importation
  11. Definition of conditional
  12. Negated conditional

Lecture Notes

• strategy.pptx or strategy.pdf

Programs

• None.

Resources

• None.

Assignments

• Practice using LogicLab.
  1. Prove definition of conditional
  2. Practice using derived rules
• Quizzes and problem sets following chapter 5 of the CMU OLI text. Due Fri. Apr. 29 at 11:59 pm.