It gives a complete set of inference rules derived from general rules given in the installment on semantics . It proves the compactness theorem from the completeness theorem for the given rule set. There are many problems at the end of the installment which give applications of the compactness theorem. The second installment contained here gives the basic results of resolution theorem proving. The course no longer follows these notes very closely.
Lectures now start with the syntax and semantics.
They then explain Skolem normal form and clausal normal form for fist order theories. It is then shown how the completeness of resolution implies the compactness theorem. The importance of the compactness theorem in establishing the expressive weakness of first order logic is emphasized.