15-317 Constructive Logic
Lecture 7: Classical Logic

In this lecture we design a judgmental formulation of classical logic based on proof by contradiction and two new judgments, A false and # (contradiction). We give several examples of classical proofs, pausing along the way to observe their structure. A common underlying theme is a certain time-travelling mind-changing behavior exhibited by classical proofs, which will become clearer when we look at the computational interpretation of classical logic.

• Reading: 07-classical.pdf
• Key concepts:
  • Proof by contradiction
  • A false judgment
  • # judgment (contradiction)
  • Contradiction principle
  • Falsity substitution principle
• Previous lecture: Natural Numbers
• Next lecture: Classical Computation

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Frank Pfenning