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
- Global soundness and completeness
- Previous lecture: Natural Deduction
- Next lecture: Proofs as Programs