Elements of Deductive Logic

Lectures: weeks 5-8.
The core EDL lectures in weeks 5 to 8 will cover the aspects of the metatheory of propositional logic specified in the Grey Book; these will be supplemented by two additional sessions, reviewing strategies for constructing metatheoretic arguments and selected material covered in the Logic Manual.

The complete handout for all lectures (with selected proofs left as exercises filled in) may be found here [.pdf, new window]

Tuesdays, 12, Lecture Room, Radcliffe Humanities.

The schedule is as follows:

Week 5: Expressive Adequacy and Interpolation. Handout. [.pdf, new window.]
DNF and CNF, DNF- and CNF-theorems; applications to expressive adequacy; interpolation theorem.

Week 6: Substitution and Duality. Handout.
Uniform substitution; substitution theorem; duality.

Week 7: Compactness. Handout.
Compactness theorem; applications.

Week 8: Soundness and Completeness. Handout.
Review of natural deduction; soundness theorem; consistent and maximal consistent sets; completeness theorem.

Additional session A. (Friday, 11, Week 5, Lecture Room.) Handout.
Review of the semantics of L1; review of metatheoretic reasoning (e.g. induction on complexity).

Additional session B. (Friday, 11, Week 7, Lecture Room.) Handout.
Review of the semantics of L2 and L=; relations.