Lec11
Where we last left.
Proofs
Important to have a standardized format.
Machine checkable.
Which is great! Definition of substitution wrong, for about ~20yrs
Hilbert, Ackermann… etc. (cf. Hilbert-Ackermann “… Logic …” book)
Substitution.
Important operation. Critical to what we have done and will do
HW: Examples of such proofs.
We had a more powerful technique. Program /equivalences/ rather than just boolean expressions.
Booleans, we had counterexamples. So far our claims that we’ve seen also give us some counterexamples.
| Booleans | Expressions | |
| Counterexamples | Generated | Can test if supplied |
| Power | Lesser | Greater |
| Decidable? | Yes | No |
| Proofs in | Trivially yes | Can be verified |