15-317 Constructive Logic
Lecture 3: Harmony

In this lecture we elaborate on the verificationist point of view that logical connectives are defined by their introduction rules. We show that for intuitionistic logic as presented so far the elimination rules are in harmony with the introduction rules in the sense that they are neither too strong nor too weak. We demonstrate this via local reductions and expansions, respectively. In the second part of the lecture we make more precise what a verification is and state, without proof, the global counterparts of the local soundness and completeness properties used to justify the elimination rules.

• Reading: 03-harmony.pdf
• Key concepts:
  • Local soundness
  • Local reduction
  • Local completeness
  • Local expansion
  • Substitution principle
  • Verifications
  • Uses
  • Global soundness and completeness
• Previous lecture: Natural Deduction
• Next lecture: Proofs as Programs

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Frank Pfenning